def test_shape_functions():
from pyrticle.tools import \
CInfinityShapeFunction, \
PolynomialShapeFunction
from hedge.mesh import \
make_uniform_1d_mesh, \
make_rect_mesh, make_box_mesh
from hedge.backends import guess_run_context
rcon = guess_run_context([])
for r in [0.1, 10]:
for mesh in [
make_uniform_1d_mesh(-r, r, 10),
make_rect_mesh(
(-r,-r), (r,r),
max_area=(r/10)**2),
make_box_mesh(
(-r,-r,-r), (r,r,r),
max_volume=(r/10)**3),
]:
discr = rcon.make_discretization(mesh, order=3)
for sfunc in [
PolynomialShapeFunction(r, discr.dimensions, 2),
PolynomialShapeFunction(r, discr.dimensions, 4),
CInfinityShapeFunction(r, discr.dimensions),
]:
num_sfunc = discr.interpolate_volume_function(
lambda x, el: sfunc(x))
int_sfunc = discr.integral(num_sfunc)
assert abs(int_sfunc-1) < 4e-5
def test_shape_functions():
from pyrticle.tools import \
CInfinityShapeFunction, \
PolynomialShapeFunction
from hedge.mesh import \
make_uniform_1d_mesh, \
make_rect_mesh, make_box_mesh
from hedge.backends import guess_run_context
rcon = guess_run_context([])
for r in [0.1, 10]:
for mesh in [
make_uniform_1d_mesh(-r, r, 10),
make_rect_mesh((-r, -r), (r, r), max_area=(r / 10)**2),
make_box_mesh((-r, -r, -r), (r, r, r), max_volume=(r / 10)**3),
]:
discr = rcon.make_discretization(mesh, order=3)
for sfunc in [
PolynomialShapeFunction(r, discr.dimensions, 2),
PolynomialShapeFunction(r, discr.dimensions, 4),
CInfinityShapeFunction(r, discr.dimensions),
]:
num_sfunc = discr.interpolate_volume_function(
lambda x, el: sfunc(x))
int_sfunc = discr.integral(num_sfunc)
assert abs(int_sfunc - 1) < 4e-5
def test_mesh_regrid():
"""Test that we are able to interpolate scalars and vectors between two
grids using a spatial binary tree."""
from math import pi, sin, cos
def some_vector(discr):
x = discr.nodes.T.astype(discr.default_scalar_type)
from hedge.tools import join_fields
u1 = discr.interpolate_volume_function(lambda x, el: sin(pi*x[0]))
u2 = discr.interpolate_volume_function(lambda x, el: sin(pi*x[1]))
u3 = discr.interpolate_volume_function(lambda x, el: sin(pi*x[0] + pi*x[1]))
u4 = discr.interpolate_volume_function(lambda x, el: cos(pi*x[0]))
return join_fields(u1, u2, u3, u4)
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.mesh.generator import make_centered_regular_rect_mesh
refine = 4
mesh = make_centered_regular_rect_mesh(
(-1, -1), (2, 2),n=(7,7), post_refine_factor=refine)
discr = rcon.make_discretization(mesh, order=6)
fields_vec = some_vector(discr)
u = discr.interpolate_volume_function(lambda x, el: sin(x[0]))
for el_per_axis in range(2,4):
for order in range(2,4):
mesh2 = make_centered_regular_rect_mesh((-1, -1), (2, 2),
n=(el_per_axis,el_per_axis), post_refine_factor=refine)
mesh_data2 = rcon.distribute_mesh(mesh2)
discr2 = rcon.make_discretization(mesh_data2, order=order)
u2 = discr2.interpolate_volume_function(lambda x, el: sin(x[0]))
fields_vec2 = some_vector(discr2)
out = discr.get_regrid_values(
u, discr2, dtype=None, use_btree=True, thresh=1e-7)
out_vec = discr.get_regrid_values(
fields_vec, discr2, dtype=None, use_btree=True, thresh=1e-7)
diff = u2 - out
diff_vec = fields_vec2 - out_vec
L2_vec=discr2.norm(diff_vec)
L2_scalar=discr2.norm(diff)
assert L2_vec < 1e-9
assert L2_scalar < 1e-9
def test_with_static_fields():
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
from hedge.discretization.local import TetrahedronDiscretization
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from hedge.discretization import Discretization
# discretization setup ----------------------------------------------------
radius = 1*units.M
full_mesh = make_cylinder_mesh(radius=radius, height=2*radius, periodic=True,
radial_subdivisions=30)
from hedge.backends import guess_run_context
pcon = guess_run_context([])
if pcon.is_head_rank:
mesh = pcon.distribute_mesh(full_mesh)
else:
mesh = pcon.receive_mesh()
discr = pcon.make_discretization(mesh, order=1)
# particles setup ---------------------------------------------------------
def get_setup(case):
c = units.VACUUM_LIGHT_SPEED()
from static_field import LarmorScrew, EBParallel
if case == "screw":
return LarmorScrew(units,
mass=units.EL_MASS, charge=units.EL_CHARGE, c=c,
vpar=c*0.8, vperp=c*0.1, bz=1e-3,
nparticles=4)
elif case == "epb":
return EBParallel(units,
mass=units.EL_MASS, charge=units.EL_CHARGE, c=c,
ez=1e+5, bz=1e-3, radius=0.5*radius, nparticles=1)
else:
raise ValueError, "invalid test case"
from pyrticle.pusher import \
MonomialParticlePusher, \
AverageParticlePusher
from static_field import run_setup
for pusher in [MonomialParticlePusher, AverageParticlePusher]:
for case in ["screw", "epb"]:
casename = "%s-%s" % (case, pusher.__class__.__name__.lower())
run_setup(units, casename, get_setup(case), discr, pusher)
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(
#["cuda"]
)
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
def boundary_tagger(vertices, el, face_nr, all_v):
return ["inflow"]
if rcon.is_head_rank:
from hedge.mesh import make_rect_mesh, \
make_centered_regular_rect_mesh
#mesh = make_rect_mesh((0,0), (10,1), max_area=0.01)
refine = 1
mesh = make_centered_regular_rect_mesh(
(0, 0),
(10, 1),
n=(20, 4),
#periodicity=(True, False),
post_refine_factor=refine,
boundary_tagger=boundary_tagger)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
shearflow = SteadyShearFlow()
fields = shearflow.volume_interpolant(0, discr)
gamma, mu, prandtl, spec_gas_const = shearflow.properties()
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=2,
gamma=gamma,
mu=mu,
prandtl=prandtl,
spec_gas_const=spec_gas_const,
bc_inflow=shearflow,
bc_outflow=shearflow,
bc_noslip=shearflow,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip")
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
# needed to get first estimate of maximum eigenvalue
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-cpu-%d-%d.dat" % (order, refine),
"w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=0.3,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 10 == 0:
#if False:
visf = vis.make_file("shearflow-%d-%04d" % (order, step))
#true_fields = shearflow.volume_interpolant(t, discr)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
],
expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "0.4*(e- 0.5*(rho_u*u))"),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
true_fields = shearflow.volume_interpolant(t, discr)
l2_error = discr.norm(op.u(fields) - op.u(true_fields))
eoc_rec.add_data_point(order, l2_error)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
finally:
vis.close()
logmgr.save()
discr.close()
def main(write_output=True,
dir_tag=TAG_NONE, neu_tag=TAG_NONE, rad_tag=TAG_ALL,
flux_type_arg="upwind", dtype=np.float64, debug=[]):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=dtype)
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE # noqa
source_center = np.array([0.1, 0.22])
source_width = 0.05
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
op = StrongWaveOperator(-1, dim,
source_f=
sym.CFunction("sin")(source_omega*sym.ScalarParameter("t"))
* sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg
)
discr = rcon.make_discretization(mesh_data, order=4, debug=debug,
default_scalar_type=dtype,
tune_for=op.op_template())
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(dtype=dtype),
[discr.volume_zeros(dtype=dtype) for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[
("u", discr.convert_volume(fields[0], kind="numpy")),
("v", discr.convert_volume(fields[1:], kind="numpy")),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
assert fields[0].dtype == dtype
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def __init__(self):
from pyrticle.units import SIUnitsWithNaturalConstants
self.units = units = SIUnitsWithNaturalConstants()
ui = PICCPyUserInterface(units)
setup = self.setup = ui.gather()
from pytools.log import LogManager
import os.path
self.logmgr = LogManager(os.path.join(setup.output_path, "pic.dat"),
"w")
from hedge.backends import guess_run_context
self.rcon = guess_run_context([])
if self.rcon.is_head_rank:
mesh = self.rcon.distribute_mesh(setup.mesh)
else:
mesh = self.rcon.receive_mesh()
self.discr = discr = \
self.rcon.make_discretization(mesh,
order=setup.element_order,
debug=setup.dg_debug)
self.logmgr.set_constant("elements_total", len(setup.mesh.elements))
self.logmgr.set_constant("elements_local", len(mesh.elements))
self.logmgr.set_constant("element_order", setup.element_order)
# em operator ---------------------------------------------------------
maxwell_kwargs = {
"epsilon": units.EPSILON0,
"mu": units.MU0,
"flux_type": setup.maxwell_flux_type,
"bdry_flux_type": setup.maxwell_bdry_flux_type
}
if discr.dimensions == 3:
from hedge.models.em import MaxwellOperator
self.maxwell_op = MaxwellOperator(**maxwell_kwargs)
elif discr.dimensions == 2:
from hedge.models.em import TEMaxwellOperator
self.maxwell_op = TEMaxwellOperator(**maxwell_kwargs)
else:
raise ValueError, "invalid mesh dimension"
if setup.chi is not None:
from pyrticle.hyperbolic import ECleaningMaxwellOperator
self.maxwell_op = ECleaningMaxwellOperator(
self.maxwell_op, chi=setup.chi, phi_decay=setup.phi_decay)
if setup.phi_filter is not None:
from pyrticle.hyperbolic import PhiFilter
from hedge.discretization import Filter, ExponentialFilterResponseFunction
em_filters.append(
PhiFilter(
maxwell_op,
Filter(
discr,
ExponentialFilterResponseFunction(
*setup.phi_filter))))
# timestepping setup --------------------------------------------------
goal_dt = self.maxwell_op.estimate_timestep(discr) * setup.dt_scale
self.nsteps = int(setup.final_time / goal_dt) + 1
self.dt = setup.final_time / self.nsteps
self.stepper = setup.timestepper_maker(self.dt)
# particle setup ------------------------------------------------------
from pyrticle.cloud import PicMethod, PicState, \
optimize_shape_bandwidth, \
guess_shape_bandwidth
method = self.method = PicMethod(
discr,
units,
setup.depositor,
setup.pusher,
dimensions_pos=setup.dimensions_pos,
dimensions_velocity=setup.dimensions_velocity,
debug=setup.debug)
self.state = method.make_state()
method.add_particles(self.state,
setup.distribution.generate_particles(),
setup.nparticles)
self.total_charge = setup.nparticles * setup.distribution.mean()[2][0]
if isinstance(setup.shape_bandwidth, str):
if setup.shape_bandwidth == "optimize":
optimize_shape_bandwidth(
method, self.state,
setup.distribution.get_rho_interpolant(
discr, self.total_charge), setup.shape_exponent)
elif setup.shape_bandwidth == "guess":
guess_shape_bandwidth(method, self.state, setup.shape_exponent)
else:
raise ValueError, "invalid shape bandwidth setting '%s'" % (
setup.shape_bandwidth)
else:
from pyrticle._internal import PolynomialShapeFunction
method.depositor.set_shape_function(
self.state,
PolynomialShapeFunction(
float(setup.shape_bandwidth),
method.mesh_data.dimensions,
setup.shape_exponent,
))
# initial condition ---------------------------------------------------
if "no_ic" in setup.debug:
self.fields = self.maxwell_op.assemble_eh(discr=discr)
else:
from pyrticle.cloud import compute_initial_condition
self.fields = compute_initial_condition(
self.rcon,
discr,
method,
self.state,
maxwell_op=self.maxwell_op,
potential_bc=setup.potential_bc,
force_zero=False)
# rhs calculators -----------------------------------------------------
from pyrticle.cloud import \
FieldRhsCalculator, \
FieldToParticleRhsCalculator, \
ParticleRhsCalculator, \
ParticleToFieldRhsCalculator
self.f_rhs_calculator = FieldRhsCalculator(self.method,
self.maxwell_op)
self.p_rhs_calculator = ParticleRhsCalculator(self.method,
self.maxwell_op)
self.f2p_rhs_calculator = FieldToParticleRhsCalculator(
self.method, self.maxwell_op)
self.p2f_rhs_calculator = ParticleToFieldRhsCalculator(
self.method, self.maxwell_op)
# instrumentation setup -----------------------------------------------
self.add_instrumentation(self.logmgr)
def main(write_output=True):
from math import sqrt, pi, exp
from os.path import join
from hedge.backends import guess_run_context
rcon = guess_run_context()
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
output_dir = "maxwell-2d"
import os
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, max_area=1e-3)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
class CurrentSource:
shape = (3, )
def __call__(self, x, el):
return [0, 0, exp(-80 * la.norm(x))]
order = 3
final_time = 1e-8
discr = rcon.make_discretization(mesh_data,
order=order,
debug=["cuda_no_plan"])
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, join(output_dir, "em-%d" % order))
if rcon.is_head_rank:
print "order %d" % order
print "#elements=", len(mesh.elements)
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.models.em import TMMaxwellOperator
from hedge.data import make_tdep_given, TimeIntervalGivenFunction
op = TMMaxwellOperator(epsilon,
mu,
flux_type=1,
current=TimeIntervalGivenFunction(
make_tdep_given(CurrentSource()),
off_time=final_time / 10),
absorb_tag=TAG_ALL,
pec_tag=TAG_NONE)
fields = op.assemble_eh(discr=discr)
from hedge.timestep import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from time import time
last_tstep = time()
t = 0
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = join(output_dir, "maxwell-%d.dat" % order)
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(
["step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max"])
# timestep loop -------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
e, h = op.split_eh(fields)
visf = vis.make_file(
join(output_dir, "em-%d-%04d" % (order, step)))
vis.add_data(visf, [
("e", discr.convert_volume(e, "numpy")),
("h", discr.convert_volume(h, "numpy")),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 0.03
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True, dtype=np.float32):
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
h_fac = 1
mesh = make_rect_mesh(a=(0, 0),
b=(1, 1),
max_area=h_fac**2 * 1e-4,
periodicity=(True, True),
subdivisions=(int(70 / h_fac), int(70 / h_fac)))
from hedge.models.gas_dynamics.lbm import \
D2Q9LBMMethod, LatticeBoltzmannOperator
op = LatticeBoltzmannOperator(D2Q9LBMMethod(), lbm_delta_t=0.001, nu=1e-4)
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data,
order=3,
default_scalar_type=dtype,
debug=["cuda_no_plan"])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(
dtype=dtype,
#vector_primitive_factory=discr.get_vector_primitive_factory()
)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.data import CompiledExpressionData
def ic_expr(t, x, fields):
from hedge.optemplate import CFunction
from pymbolic.primitives import IfPositive
from pytools.obj_array import make_obj_array
tanh = CFunction("tanh")
sin = CFunction("sin")
rho = 1
u0 = 0.05
w = 0.05
delta = 0.05
from hedge.optemplate.primitives import make_common_subexpression as cse
u = cse(
make_obj_array([
IfPositive(x[1] - 1 / 2, u0 * tanh(4 * (3 / 4 - x[1]) / w),
u0 * tanh(4 * (x[1] - 1 / 4) / w)),
u0 * delta * sin(2 * np.pi * (x[0] + 1 / 4))
]), "u")
return make_obj_array([
op.method.f_equilibrium(rho, alpha, u)
for alpha in range(len(op.method))
])
# timestep loop -----------------------------------------------------------
stream_rhs = op.bind_rhs(discr)
collision_update = op.bind(discr, op.collision_update)
get_rho = op.bind(discr, op.rho)
get_rho_u = op.bind(discr, op.rho_u)
f_bar = CompiledExpressionData(ic_expr).volume_interpolant(0, discr)
from hedge.discretization import ExponentialFilterResponseFunction
from hedge.optemplate.operators import FilterOperator
mode_filter = FilterOperator(
ExponentialFilterResponseFunction(min_amplification=0.9, order=4))\
.bind(discr)
final_time = 1000
try:
lbm_dt = op.lbm_delta_t
dg_dt = op.estimate_timestep(discr, stepper=stepper)
print dg_dt
dg_steps_per_lbm_step = int(np.ceil(lbm_dt / dg_dt))
dg_dt = lbm_dt / dg_steps_per_lbm_step
lbm_steps = int(final_time // op.lbm_delta_t)
for step in xrange(lbm_steps):
t = step * lbm_dt
if step % 100 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
rho = get_rho(f_bar)
rho_u = get_rho_u(f_bar)
vis.add_data(
visf,
[("fbar%d" % i, discr.convert_volume(f_bar_i, "numpy"))
for i, f_bar_i in enumerate(f_bar)] + [
("rho", discr.convert_volume(rho, "numpy")),
("rho_u", discr.convert_volume(rho_u, "numpy")),
],
time=t,
step=step)
visf.close()
print "step=%d, t=%f" % (step, t)
f_bar = collision_update(f_bar)
for substep in range(dg_steps_per_lbm_step):
f_bar = stepper(f_bar, t + substep * dg_dt, dg_dt, stream_rhs)
#f_bar = mode_filter(f_bar)
finally:
if write_output:
vis.close()
discr.close()
def test_efield_vs_gauss_law():
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from math import sqrt, pi
from pytools.arithmetic_container import \
ArithmeticList, join_fields
from random import seed
from pytools.stopwatch import Job
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
seed(0)
nparticles = 10000
beam_radius = 2.5 * units.MM
emittance = 5 * units.MM * units.MRAD
final_time = 0.1 * units.M / units.VACUUM_LIGHT_SPEED()
field_dump_interval = 1
tube_length = 20 * units.MM
# discretization setup ----------------------------------------------------
from pyrticle.geometry import make_cylinder_with_fine_core
mesh = make_cylinder_with_fine_core(
r=10 * beam_radius,
inner_r=1 * beam_radius,
min_z=0,
max_z=tube_length,
max_volume_inner=10 * units.MM**3,
max_volume_outer=100 * units.MM**3,
radial_subdiv=10,
)
from hedge.backends import guess_run_context
rcon = guess_run_context([])
discr = rcon.make_discretization(mesh, order=3)
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(epsilon=units.EPSILON0, mu=units.MU0, flux_type=1)
from hedge.models.nd_calculus import DivergenceOperator
div_op = DivergenceOperator(discr.dimensions)
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units, ShapeFunctionDepositor(),
MonomialParticlePusher(), 3, 3)
# particle ic ---------------------------------------------------------
cloud_charge = -1e-9 * units.C
electrons_per_particle = abs(cloud_charge / nparticles / units.EL_CHARGE)
el_energy = 10 * units.EL_REST_ENERGY()
el_lorentz_gamma = el_energy / units.EL_REST_ENERGY()
beta = (1 - 1 / el_lorentz_gamma**2)**0.5
gamma = 1 / sqrt(1 - beta**2)
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units,
total_charge=cloud_charge,
p_charge=cloud_charge / nparticles,
p_mass=electrons_per_particle * units.EL_MASS,
radii=2 * [beam_radius],
emittances=2 * [5 * units.MM * units.MRAD],
z_length=tube_length,
z_pos=tube_length / 2,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# field ic ----------------------------------------------------------------
from pyrticle.cloud import guess_shape_bandwidth
guess_shape_bandwidth(method, state, 2)
from pyrticle.cloud import compute_initial_condition
from hedge.data import ConstantGivenFunction
fields = compute_initial_condition(rcon,
discr,
method,
state,
maxwell_op=max_op,
potential_bc=ConstantGivenFunction())
# check against theory ----------------------------------------------------
q_per_unit_z = cloud_charge / beam.z_length
class TheoreticalEField:
shape = (3, )
def __call__(self, x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
xy_unit = x / r
xy_unit[2] = 0
return xy_unit * ((q_per_unit_z) /
(2 * pi * r * max_op.epsilon))
else:
return numpy.zeros((3, ))
def theory_indicator(x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
return 1
else:
return 0
from hedge.tools import join_fields, to_obj_array
e_theory = to_obj_array(
discr.interpolate_volume_function(TheoreticalEField()))
theory_ind = discr.interpolate_volume_function(theory_indicator)
e_field, h_field = max_op.split_eh(fields)
restricted_e = join_fields(*[e_i * theory_ind for e_i in e_field])
def l2_error(field, true):
return discr.norm(field - true) / discr.norm(true)
outer_l2 = l2_error(restricted_e, e_theory)
assert outer_l2 < 0.08
if False:
visf = vis.make_file("e_comparison")
mesh_scalars, mesh_vectors = \
method.add_to_vis(vis, visf)
vis.add_data(visf, [
("e", restricted_e),
("e_theory", e_theory),
] + mesh_vectors + mesh_scalars)
visf.close()
def __init__(self):
from pyrticle.units import SIUnitsWithNaturalConstants
self.units = units = SIUnitsWithNaturalConstants()
ui = PICCPyUserInterface(units)
setup = self.setup = ui.gather()
from pytools.log import LogManager
import os.path
self.logmgr = LogManager(os.path.join(
setup.output_path, "pic.dat"), "w")
from hedge.backends import guess_run_context
self.rcon = guess_run_context([])
if self.rcon.is_head_rank:
mesh = self.rcon.distribute_mesh(setup.mesh)
else:
mesh = self.rcon.receive_mesh()
self.discr = discr = \
self.rcon.make_discretization(mesh,
order=setup.element_order,
debug=setup.dg_debug)
self.logmgr.set_constant("elements_total", len(setup.mesh.elements))
self.logmgr.set_constant("elements_local", len(mesh.elements))
self.logmgr.set_constant("element_order", setup.element_order)
# em operator ---------------------------------------------------------
maxwell_kwargs = {
"epsilon": units.EPSILON0,
"mu": units.MU0,
"flux_type": setup.maxwell_flux_type,
"bdry_flux_type": setup.maxwell_bdry_flux_type
}
if discr.dimensions == 3:
from hedge.models.em import MaxwellOperator
self.maxwell_op = MaxwellOperator(**maxwell_kwargs)
elif discr.dimensions == 2:
from hedge.models.em import TEMaxwellOperator
self.maxwell_op = TEMaxwellOperator(**maxwell_kwargs)
else:
raise ValueError, "invalid mesh dimension"
if setup.chi is not None:
from pyrticle.hyperbolic import ECleaningMaxwellOperator
self.maxwell_op = ECleaningMaxwellOperator(self.maxwell_op,
chi=setup.chi,
phi_decay=setup.phi_decay)
if setup.phi_filter is not None:
from pyrticle.hyperbolic import PhiFilter
from hedge.discretization import Filter, ExponentialFilterResponseFunction
em_filters.append(
PhiFilter(maxwell_op, Filter(discr,
ExponentialFilterResponseFunction(*setup.phi_filter))))
# timestepping setup --------------------------------------------------
goal_dt = self.maxwell_op.estimate_timestep(discr) * setup.dt_scale
self.nsteps = int(setup.final_time/goal_dt)+1
self.dt = setup.final_time/self.nsteps
self.stepper = setup.timestepper_maker(self.dt)
# particle setup ------------------------------------------------------
from pyrticle.cloud import PicMethod, PicState, \
optimize_shape_bandwidth, \
guess_shape_bandwidth
method = self.method = PicMethod(discr, units,
setup.depositor, setup.pusher,
dimensions_pos=setup.dimensions_pos,
dimensions_velocity=setup.dimensions_velocity,
debug=setup.debug)
self.state = method.make_state()
method.add_particles(
self.state,
setup.distribution.generate_particles(),
setup.nparticles)
self.total_charge = setup.nparticles*setup.distribution.mean()[2][0]
if isinstance(setup.shape_bandwidth, str):
if setup.shape_bandwidth == "optimize":
optimize_shape_bandwidth(method, self.state,
setup.distribution.get_rho_interpolant(
discr, self.total_charge),
setup.shape_exponent)
elif setup.shape_bandwidth == "guess":
guess_shape_bandwidth(method, self.state, setup.shape_exponent)
else:
raise ValueError, "invalid shape bandwidth setting '%s'" % (
setup.shape_bandwidth)
else:
from pyrticle._internal import PolynomialShapeFunction
method.depositor.set_shape_function(
self.state,
PolynomialShapeFunction(
float(setup.shape_bandwidth),
method.mesh_data.dimensions,
setup.shape_exponent,
))
# initial condition ---------------------------------------------------
if "no_ic" in setup.debug:
self.fields = self.maxwell_op.assemble_eh(discr=discr)
else:
from pyrticle.cloud import compute_initial_condition
self.fields = compute_initial_condition(self.rcon, discr, method, self.state,
maxwell_op=self.maxwell_op,
potential_bc=setup.potential_bc,
force_zero=False)
# rhs calculators -----------------------------------------------------
from pyrticle.cloud import \
FieldRhsCalculator, \
FieldToParticleRhsCalculator, \
ParticleRhsCalculator, \
ParticleToFieldRhsCalculator
self.f_rhs_calculator = FieldRhsCalculator(self.method, self.maxwell_op)
self.p_rhs_calculator = ParticleRhsCalculator(self.method, self.maxwell_op)
self.f2p_rhs_calculator = FieldToParticleRhsCalculator(self.method, self.maxwell_op)
self.p2f_rhs_calculator = ParticleToFieldRhsCalculator(self.method, self.maxwell_op)
# instrumentation setup -----------------------------------------------
self.add_instrumentation(self.logmgr)
def main(write_output=True,
allow_features=None,
flux_type_arg=1,
bdry_flux_type_arg=None,
extra_discr_args={}):
from hedge.mesh.generator import make_cylinder_mesh, make_box_mesh
from hedge.tools import EOCRecorder, to_obj_array
from math import sqrt, pi # noqa
from analytic_solutions import ( # noqa
RealPartAdapter, SplitComplexAdapter, CylindricalFieldAdapter,
CylindricalCavityMode, RectangularWaveguideMode, RectangularCavityMode)
from hedge.models.em import MaxwellOperator
logging.basicConfig(level=logging.DEBUG)
from hedge.backends import guess_run_context
rcon = guess_run_context(allow_features)
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
eoc_rec = EOCRecorder()
cylindrical = False
periodic = False
if cylindrical:
R = 1
d = 2
mode = CylindricalCavityMode(m=1,
n=1,
p=1,
radius=R,
height=d,
epsilon=epsilon,
mu=mu)
# r_sol = CylindricalFieldAdapter(RealPartAdapter(mode))
# c_sol = SplitComplexAdapter(CylindricalFieldAdapter(mode))
if rcon.is_head_rank:
mesh = make_cylinder_mesh(radius=R, height=d, max_volume=0.01)
else:
if periodic:
mode = RectangularWaveguideMode(epsilon, mu, (3, 2, 1))
periodicity = (False, False, True)
else:
periodicity = None
mode = RectangularCavityMode(epsilon, mu, (1, 2, 2))
if rcon.is_head_rank:
mesh = make_box_mesh(max_volume=0.001, periodicity=periodicity)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [4, 5, 6]:
#for order in [1,2,3,4,5,6]:
extra_discr_args.setdefault("debug", []).extend(
["cuda_no_plan", "cuda_dump_kernels"])
op = MaxwellOperator(epsilon,
mu,
flux_type=flux_type_arg,
bdry_flux_type=bdry_flux_type_arg)
discr = rcon.make_discretization(mesh_data,
order=order,
tune_for=op.op_template(),
**extra_discr_args)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
mode.set_time(0)
def get_true_field():
return discr.convert_volume(to_obj_array(
mode(discr).real.astype(discr.default_scalar_type).copy()),
kind=discr.compute_kind)
fields = get_true_field()
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type, rcon=rcon)
#from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = Dumka3TimeStepper(3, dtype=discr.default_scalar_type, rcon=rcon)
# {{{ diagnostics setup
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "maxwell-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(
["step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
final_time = 0.5e-9
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 50 == 0 and write_output:
sub_timer = vis_timer.start_sub_timer()
e, h = op.split_eh(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
vis.add_data(visf, [
("e", discr.convert_volume(e, kind="numpy")),
("h", discr.convert_volume(h, kind="numpy")),
],
time=t,
step=step)
visf.close()
sub_timer.stop().submit()
fields = stepper(fields, t, dt, rhs)
mode.set_time(final_time)
eoc_rec.add_data_point(order,
discr.norm(fields - get_true_field()))
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
if rcon.is_head_rank:
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
# }}}
assert eoc_rec.estimate_order_of_convergence()[0, 1] > 6
def main(final_time=1, write_output=False):
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from hedge.mesh import make_box_mesh
mesh = make_box_mesh((0,0,0), (10,10,10), max_volume=0.5)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3, 4, 5]:
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "sinewave-%d" % order)
#vis = SiloVisualizer(discr, rcon)
sinewave = SineWave()
fields = sinewave.volume_interpolant(0, discr)
gamma, mu, prandtl, spec_gas_const = sinewave.properties()
from hedge.mesh import TAG_ALL
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=mesh.dimensions, gamma=gamma, mu=mu,
prandtl=prandtl, spec_gas_const=spec_gas_const,
bc_inflow=sinewave, bc_outflow=sinewave, bc_noslip=sinewave,
inflow_tag=TAG_ALL, source=None)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_name = ("euler-sinewave-%(order)d-%(els)d.dat"
% {"order":order, "els":len(mesh.elements)})
else:
log_name = False
logmgr = LogManager(log_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
#if step % 10 == 0:
if write_output:
visf = vis.make_file("sinewave-%d-%04d" % (order, step))
#from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", op.rho(true_fields)),
#("true_e", op.e(true_fields)),
#("true_rho_u", op.rho_u(true_fields)),
#("true_u", op.u(true_fields)),
#("rhs_rho", op.rho(rhs_fields)),
#("rhs_e", op.e(rhs_fields)),
#("rhs_rho_u", op.rho_u(rhs_fields)),
],
#expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
#("p", "0.4*(e- 0.5*(rho_u*u))"),
#],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
finally:
vis.close()
logmgr.close()
discr.close()
true_fields = sinewave.volume_interpolant(t, discr)
eoc_rec.add_data_point(order, discr.norm(fields-true_fields))
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
def main():
import logging
logging.basicConfig(level=logging.INFO)
from hedge.backends import guess_run_context
rcon = guess_run_context()
if rcon.is_head_rank:
if True:
mesh = make_squaremesh()
else:
from hedge.mesh import make_rect_mesh
mesh = make_rect_mesh(
boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"],
max_area=0.1)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script(".")
for order in [3]:
from gas_dynamics_initials import UniformMachFlow
square = UniformMachFlow(gaussian_pulse_at=numpy.array([-2, 2]),
pulse_magnitude=0.003)
from hedge.models.gas_dynamics import (
GasDynamicsOperator,
GammaLawEOS)
op = GasDynamicsOperator(dimensions=2,
equation_of_state=GammaLawEOS(square.gamma), mu=square.mu,
prandtl=square.prandtl, spec_gas_const=square.spec_gas_const,
bc_inflow=square, bc_outflow=square, bc_noslip=square,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
discr = rcon.make_discretization(mesh_data, order=order,
debug=["cuda_no_plan",
"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"dump_op_code"
#"cuda_no_plan_el_local"
],
default_scalar_type=numpy.float64,
tune_for=op.op_template(),
quad_min_degrees={
"gasdyn_vol": 3*order,
"gasdyn_face": 3*order,
}
)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
from hedge.timestep.runge_kutta import (
LSRK4TimeStepper, ODE23TimeStepper, ODE45TimeStepper)
from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type,
#vector_primitive_factory=discr.get_vector_primitive_factory())
stepper = ODE23TimeStepper(dtype=discr.default_scalar_type,
rtol=1e-6,
vector_primitive_factory=discr.get_vector_primitive_factory())
# Dumka works kind of poorly
#stepper = Dumka3TimeStepper(dtype=discr.default_scalar_type,
#rtol=1e-7, pol_index=2,
#vector_primitive_factory=discr.get_vector_primitive_factory())
#from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = Dumka3TimeStepper(3, rtol=1e-7)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("cns-square-sp-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1", "Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
#logmgr.add_quantity(ChangeSinceLastStep())
add_simulation_quantities(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# filter setup ------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(discr,
ExponentialFilterResponseFunction(min_amplification=0.95, order=6))
# timestep loop -------------------------------------------------------
fields = square.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1000,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: next_dt,
taken_dt_getter=lambda: taken_dt)
model_stepper = LSRK4TimeStepper()
next_dt = op.estimate_timestep(discr,
stepper=model_stepper, t=0,
max_eigenvalue=max_eigval[0])
for step, t, dt in step_it:
#if (step % 10000 == 0): #and step < 950000) or (step % 500 == 0 and step > 950000):
#if False:
if step % 5 == 0:
visf = vis.make_file("square-%d-%06d" % (order, step))
#from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
if stepper.adaptive:
fields, t, taken_dt, next_dt = stepper(fields, t, dt, rhs)
else:
taken_dt = dt
fields = stepper(fields, t, dt, rhs)
dt = op.estimate_timestep(discr,
stepper=model_stepper, t=0,
max_eigenvalue=max_eigval[0])
#fields = mode_filter(fields)
finally:
vis.close()
logmgr.save()
discr.close()
def test_cuda_volume_quadrature():
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-1,-1),b=(1,1),max_area=0.08)
from hedge.backends import guess_run_context
cpu_rcon = guess_run_context(['jit'])
gpu_rcon = guess_run_context(['cuda'])
order = 4
quad_min_degrees = {"quad": 3*order}
cpu_discr, gpu_discr = [
rcon.make_discretization(mesh, order=order,
default_scalar_type=numpy.float64,
debug=["cuda_no_plan", "cuda_no_microblock", ],
quad_min_degrees=quad_min_degrees
)
for rcon in [cpu_rcon, gpu_rcon]]
from math import sin, cos
def f(x, el):
return sin(x[0])*cos(x[1])
cpu_field, gpu_field = [
discr.interpolate_volume_function(f)
for discr in [cpu_discr, gpu_discr]]
def make_optemplate():
from hedge.optemplate.operators import QuadratureGridUpsampler
from hedge.optemplate import Field, make_stiffness_t
u = Field("u")
qu = QuadratureGridUpsampler("quad")(u)
return make_stiffness_t(2)[0](Field("intercept")(qu))
saved_vectors = []
def intercept(x):
saved_vectors.append(x)
return x
for discr in [cpu_discr, gpu_discr]:
discr.add_function("intercept", intercept)
opt = make_optemplate()
cpu_bound, gpu_bound = [discr.compile(make_optemplate())
for discr in [cpu_discr, gpu_discr]]
cpu_result = cpu_bound(u=cpu_field)
gpu_result = gpu_bound(u=gpu_field)
cpu_ivec, gpu_ivec = saved_vectors
gpu_ivec_on_host = gpu_ivec.get()[gpu_discr._gpu_volume_embedding("quad")]
ierr = cpu_ivec-gpu_ivec_on_host
assert la.norm(ierr) < 5e-15
gpu_result_on_host = gpu_discr.convert_volume(gpu_result, kind="numpy")
err = cpu_result-gpu_result_on_host
assert la.norm(err) < 2e-14
cpu_discr.close()
gpu_discr.close()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(["cuda"])
if rcon.is_head_rank:
mesh = make_boxmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
box = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=box.gamma,
mu=box.mu,
prandtl=box.prandtl,
spec_gas_const=box.spec_gas_const,
bc_inflow=box,
bc_outflow=box,
bc_noslip=box,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip")
discr = rcon.make_discretization(
mesh_data,
order=order,
debug=[
#"cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code",
"cuda_no_plan_el_local",
],
default_scalar_type=numpy.float32,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer # noqa
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = box.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w",
rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1",
"Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
logmgr.add_quantity(ChangeSinceLastStep())
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("box-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
# ("rhs_rho", discr.convert_volume(
# op.rho(rhs_fields), kind="numpy")),
# ("rhs_e", discr.convert_volume(
# op.e(rhs_fields), kind="numpy")),
# ("rhs_rho_u", discr.convert_volume(
# op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
finally:
vis.close()
logmgr.save()
discr.close()
def main(write_output=True, flux_type_arg="upwind"):
from hedge.tools import mem_checkpoint
from math import sin, cos, pi, sqrt
from math import floor
from hedge.backends import guess_run_context
rcon = guess_run_context()
def f(x):
return sin(pi * x)
def u_analytic(x, el, t):
return f((-numpy.dot(v, x) / norm_v + t * norm_v))
def boundary_tagger(vertices, el, face_nr, all_v):
if numpy.dot(el.face_normals[face_nr], v) < 0:
return ["inflow"]
else:
return ["outflow"]
dim = 2
if dim == 1:
v = numpy.array([1])
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(0, 2, 10, periodic=True)
elif dim == 2:
v = numpy.array([2, 0])
if rcon.is_head_rank:
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(boundary_tagger=boundary_tagger)
elif dim == 3:
v = numpy.array([0, 0, 1])
if rcon.is_head_rank:
from hedge.mesh.generator import make_cylinder_mesh, make_ball_mesh, make_box_mesh
mesh = make_cylinder_mesh(max_volume=0.04,
height=2,
boundary_tagger=boundary_tagger,
periodic=False,
radial_subdivisions=32)
else:
raise RuntimeError, "bad number of dimensions"
norm_v = la.norm(v)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
if dim != 1:
mesh_data = mesh_data.reordered_by("cuthill")
discr = rcon.make_discretization(mesh_data, order=4)
vis_discr = discr
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(vis_discr, rcon, "fld")
# operator setup ----------------------------------------------------------
from hedge.data import \
ConstantGivenFunction, \
TimeConstantGivenFunction, \
TimeDependentGivenFunction
from hedge.models.advection import StrongAdvectionOperator, WeakAdvectionOperator
op = WeakAdvectionOperator(v,
inflow_u=TimeDependentGivenFunction(u_analytic),
flux_type=flux_type_arg)
u = discr.interpolate_volume_function(lambda x, el: u_analytic(x, el, 0))
# timestep setup ----------------------------------------------------------
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
if rcon.is_head_rank:
print "%d elements" % len(discr.mesh.elements)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "advection.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from hedge.log import Integral, LpNorm
u_getter = lambda: u
logmgr.add_quantity(Integral(u_getter, discr, name="int_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, p=1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=3,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
if step % 5 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(u, kind="numpy")),
],
time=t,
step=step)
visf.close()
u = stepper(u, t, dt, rhs)
true_u = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, t))
print discr.norm(u - true_u)
assert discr.norm(u - true_u) < 1e-2
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True):
from math import sqrt, pi, exp
from os.path import join
from hedge.backends import guess_run_context
rcon = guess_run_context()
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4*pi*1e-7 # N/A**2.
epsilon = 1*epsilon0
mu = 1*mu0
output_dir = "maxwell-2d"
import os
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, max_area=1e-3)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
class CurrentSource:
shape = (3,)
def __call__(self, x, el):
return [0,0,exp(-80*la.norm(x))]
order = 3
final_time = 1e-8
discr = rcon.make_discretization(mesh_data, order=order,
debug=["cuda_no_plan"])
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, join(output_dir, "em-%d" % order))
if rcon.is_head_rank:
print "order %d" % order
print "#elements=", len(mesh.elements)
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.models.em import TMMaxwellOperator
from hedge.data import make_tdep_given, TimeIntervalGivenFunction
op = TMMaxwellOperator(epsilon, mu, flux_type=1,
current=TimeIntervalGivenFunction(
make_tdep_given(CurrentSource()), off_time=final_time/10),
absorb_tag=TAG_ALL, pec_tag=TAG_NONE)
fields = op.assemble_eh(discr=discr)
from hedge.timestep import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from time import time
last_tstep = time()
t = 0
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = join(output_dir, "maxwell-%d.dat" % order)
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(["step.max", "t_sim.max",
("W_field", "W_el+W_mag"), "t_step.max"])
# timestep loop -------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
e, h = op.split_eh(fields)
visf = vis.make_file(join(output_dir, "em-%d-%04d" % (order, step)))
vis.add_data(visf,
[
("e", discr.convert_volume(e, "numpy")),
("h", discr.convert_volume(h, "numpy")),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 0.03
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True, flux_type_arg="upwind"):
from hedge.tools import mem_checkpoint
from math import sin, cos, pi, sqrt
from math import floor
from hedge.backends import guess_run_context
rcon = guess_run_context()
def f(x):
return sin(pi*x)
def u_analytic(x, el, t):
return f((-numpy.dot(v, x)/norm_v+t*norm_v))
def boundary_tagger(vertices, el, face_nr, all_v):
if numpy.dot(el.face_normals[face_nr], v) < 0:
return ["inflow"]
else:
return ["outflow"]
dim = 2
if dim == 1:
v = numpy.array([1])
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(0, 2, 10, periodic=True)
elif dim == 2:
v = numpy.array([2,0])
if rcon.is_head_rank:
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(boundary_tagger=boundary_tagger)
elif dim == 3:
v = numpy.array([0,0,1])
if rcon.is_head_rank:
from hedge.mesh.generator import make_cylinder_mesh, make_ball_mesh, make_box_mesh
mesh = make_cylinder_mesh(max_volume=0.04, height=2, boundary_tagger=boundary_tagger,
periodic=False, radial_subdivisions=32)
else:
raise RuntimeError, "bad number of dimensions"
norm_v = la.norm(v)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
if dim != 1:
mesh_data = mesh_data.reordered_by("cuthill")
discr = rcon.make_discretization(mesh_data, order=4)
vis_discr = discr
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(vis_discr, rcon, "fld")
# operator setup ----------------------------------------------------------
from hedge.data import \
ConstantGivenFunction, \
TimeConstantGivenFunction, \
TimeDependentGivenFunction
from hedge.models.advection import StrongAdvectionOperator, WeakAdvectionOperator
op = WeakAdvectionOperator(v,
inflow_u=TimeDependentGivenFunction(u_analytic),
flux_type=flux_type_arg)
u = discr.interpolate_volume_function(lambda x, el: u_analytic(x, el, 0))
# timestep setup ----------------------------------------------------------
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
if rcon.is_head_rank:
print "%d elements" % len(discr.mesh.elements)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "advection.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from hedge.log import Integral, LpNorm
u_getter = lambda: u
logmgr.add_quantity(Integral(u_getter, discr, name="int_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, p=1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=3, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
if step % 5 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(u, kind="numpy")),
], time=t, step=step)
visf.close()
u = stepper(u, t, dt, rhs)
true_u = discr.interpolate_volume_function(lambda x, el: u_analytic(x, el, t))
print discr.norm(u-true_u)
assert discr.norm(u-true_u) < 1e-2
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def test_efield_vs_gauss_law():
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from math import sqrt, pi
from pytools.arithmetic_container import \
ArithmeticList, join_fields
from random import seed
from pytools.stopwatch import Job
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
seed(0)
nparticles = 10000
beam_radius = 2.5 * units.MM
emittance = 5 * units.MM * units.MRAD
final_time = 0.1*units.M/units.VACUUM_LIGHT_SPEED()
field_dump_interval = 1
tube_length = 20*units.MM
# discretization setup ----------------------------------------------------
from pyrticle.geometry import make_cylinder_with_fine_core
mesh = make_cylinder_with_fine_core(
r=10*beam_radius, inner_r=1*beam_radius,
min_z=0, max_z=tube_length,
max_volume_inner=10*units.MM**3,
max_volume_outer=100*units.MM**3,
radial_subdiv=10,
)
from hedge.backends import guess_run_context
rcon = guess_run_context([])
discr = rcon.make_discretization(mesh, order=3)
from hedge.models.em import MaxwellOperator
max_op = MaxwellOperator(
epsilon=units.EPSILON0,
mu=units.MU0,
flux_type=1)
from hedge.models.nd_calculus import DivergenceOperator
div_op = DivergenceOperator(discr.dimensions)
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units,
ShapeFunctionDepositor(),
MonomialParticlePusher(),
3, 3)
# particle ic ---------------------------------------------------------
cloud_charge = -1e-9 * units.C
electrons_per_particle = abs(cloud_charge/nparticles/units.EL_CHARGE)
el_energy = 10*units.EL_REST_ENERGY()
el_lorentz_gamma = el_energy/units.EL_REST_ENERGY()
beta = (1-1/el_lorentz_gamma**2)**0.5
gamma = 1/sqrt(1-beta**2)
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units, total_charge=cloud_charge,
p_charge=cloud_charge/nparticles,
p_mass=electrons_per_particle*units.EL_MASS,
radii=2*[beam_radius],
emittances=2*[5 * units.MM * units.MRAD],
z_length=tube_length,
z_pos=tube_length/2,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# field ic ----------------------------------------------------------------
from pyrticle.cloud import guess_shape_bandwidth
guess_shape_bandwidth(method, state, 2)
from pyrticle.cloud import compute_initial_condition
from hedge.data import ConstantGivenFunction
fields = compute_initial_condition(
rcon,
discr, method, state, maxwell_op=max_op,
potential_bc=ConstantGivenFunction())
# check against theory ----------------------------------------------------
q_per_unit_z = cloud_charge/beam.z_length
class TheoreticalEField:
shape = (3,)
def __call__(self, x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
xy_unit = x/r
xy_unit[2] = 0
return xy_unit*((q_per_unit_z)
/
(2*pi*r*max_op.epsilon))
else:
return numpy.zeros((3,))
def theory_indicator(x, el):
r = la.norm(x[:2])
if r >= max(beam.radii):
return 1
else:
return 0
from hedge.tools import join_fields, to_obj_array
e_theory = to_obj_array(discr.interpolate_volume_function(TheoreticalEField()))
theory_ind = discr.interpolate_volume_function(theory_indicator)
e_field, h_field = max_op.split_eh(fields)
restricted_e = join_fields(*[e_i * theory_ind for e_i in e_field])
def l2_error(field, true):
return discr.norm(field-true)/discr.norm(true)
outer_l2 = l2_error(restricted_e, e_theory)
assert outer_l2 < 0.08
if False:
visf = vis.make_file("e_comparison")
mesh_scalars, mesh_vectors = \
method.add_to_vis(vis, visf)
vis.add_data(visf, [
("e", restricted_e),
("e_theory", e_theory),
]
+ mesh_vectors
+ mesh_scalars
)
visf.close()
def main(final_time=1, write_output=False):
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from hedge.mesh import make_box_mesh
mesh = make_box_mesh((0, 0, 0), (10, 10, 10), max_volume=0.5)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3, 4, 5]:
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "sinewave-%d" % order)
#vis = SiloVisualizer(discr, rcon)
sinewave = SineWave()
fields = sinewave.volume_interpolant(0, discr)
gamma, mu, prandtl, spec_gas_const = sinewave.properties()
from hedge.mesh import TAG_ALL
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=mesh.dimensions,
gamma=gamma,
mu=mu,
prandtl=prandtl,
spec_gas_const=spec_gas_const,
bc_inflow=sinewave,
bc_outflow=sinewave,
bc_noslip=sinewave,
inflow_tag=TAG_ALL,
source=None)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_name = ("euler-sinewave-%(order)d-%(els)d.dat" % {
"order": order,
"els": len(mesh.elements)
})
else:
log_name = False
logmgr = LogManager(log_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
#if step % 10 == 0:
if write_output:
visf = vis.make_file("sinewave-%d-%04d" % (order, step))
#from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", op.rho(true_fields)),
#("true_e", op.e(true_fields)),
#("true_rho_u", op.rho_u(true_fields)),
#("true_u", op.u(true_fields)),
#("rhs_rho", op.rho(rhs_fields)),
#("rhs_e", op.e(rhs_fields)),
#("rhs_rho_u", op.rho_u(rhs_fields)),
],
#expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
#("p", "0.4*(e- 0.5*(rho_u*u))"),
#],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
finally:
vis.close()
logmgr.close()
discr.close()
true_fields = sinewave.volume_interpolant(t, discr)
eoc_rec.add_data_point(order, discr.norm(fields - true_fields))
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
def main(write_output=True):
from hedge.timestep import RK4TimeStepper
from hedge.mesh import make_disk_mesh
from math import sqrt, pi, exp
from hedge.backends import guess_run_context, FEAT_CUDA
rcon = guess_run_context()
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4*pi*1e-7 # N/A**2.
epsilon = 1*epsilon0
mu = 1*mu0
c = 1/sqrt(mu*epsilon)
cylindrical = False
periodic = False
pml_width = 0.5
#mesh = make_mesh(a=numpy.array((-1,-1,-1)), b=numpy.array((1,1,1)),
#mesh = make_mesh(a=numpy.array((-3,-3)), b=numpy.array((3,3)),
mesh = make_mesh(a=numpy.array((-1,-1)), b=numpy.array((1,1)),
#mesh = make_mesh(a=numpy.array((-2,-2)), b=numpy.array((2,2)),
pml_width=pml_width, max_volume=0.01)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
class Current:
def volume_interpolant(self, t, discr):
from hedge.tools import make_obj_array
result = discr.volume_zeros(kind="numpy", dtype=numpy.float64)
omega = 6*c
if omega*t > 2*pi:
return make_obj_array([result, result, result])
x = make_obj_array(discr.nodes.T)
r = numpy.sqrt(numpy.dot(x, x))
idx = r<0.3
result[idx] = (1+numpy.cos(pi*r/0.3))[idx] \
*numpy.sin(omega*t)**3
result = discr.convert_volume(result, kind=discr.compute_kind,
dtype=discr.default_scalar_type)
return make_obj_array([-result, result, result])
order = 3
discr = rcon.make_discretization(mesh_data, order=order,
debug=["cuda_no_plan"])
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.data import GivenFunction, TimeHarmonicGivenFunction, TimeIntervalGivenFunction
from hedge.models.em import MaxwellOperator
from hedge.models.pml import \
AbarbanelGottliebPMLMaxwellOperator, \
AbarbanelGottliebPMLTMMaxwellOperator, \
AbarbanelGottliebPMLTEMaxwellOperator
op = AbarbanelGottliebPMLTEMaxwellOperator(epsilon, mu, flux_type=1,
current=Current(),
pec_tag=TAG_ALL,
absorb_tag=TAG_NONE,
add_decay=True
)
fields = op.assemble_ehpq(discr=discr)
stepper = RK4TimeStepper()
if rcon.is_head_rank:
print "order %d" % order
print "#elements=", len(mesh.elements)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "maxwell-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(["step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max"])
from hedge.log import LpNorm
class FieldIdxGetter:
def __init__(self, whole_getter, idx):
self.whole_getter = whole_getter
self.idx = idx
def __call__(self):
return self.whole_getter()[self.idx]
# timestep loop -------------------------------------------------------
t = 0
pml_coeff = op.coefficients_from_width(discr, width=pml_width)
rhs = op.bind(discr, pml_coeff)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4/c, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
e, h, p, q = op.split_ehpq(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
#pml_rhs_e, pml_rhs_h, pml_rhs_p, pml_rhs_q = \
#op.split_ehpq(rhs(t, fields))
j = Current().volume_interpolant(t, discr)
vis.add_data(visf, [
("e", discr.convert_volume(e, "numpy")),
("h", discr.convert_volume(h, "numpy")),
("p", discr.convert_volume(p, "numpy")),
("q", discr.convert_volume(q, "numpy")),
("j", discr.convert_volume(j, "numpy")),
#("pml_rhs_e", pml_rhs_e),
#("pml_rhs_h", pml_rhs_h),
#("pml_rhs_p", pml_rhs_p),
#("pml_rhs_q", pml_rhs_q),
#("max_rhs_e", max_rhs_e),
#("max_rhs_h", max_rhs_h),
#("max_rhs_p", max_rhs_p),
#("max_rhs_q", max_rhs_q),
],
time=t, step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
_, _, energies_data = logmgr.get_expr_dataset("W_el+W_mag")
energies = [value for tick_nbr, value in energies_data]
assert energies[-1] < max(energies) * 1e-2
finally:
logmgr.close()
if write_output:
vis.close()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context( ["cuda", "mpi"])
if rcon.is_head_rank:
mesh = make_wingmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
wing = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=wing.gamma, mu=wing.mu,
prandtl=wing.prandtl, spec_gas_const=wing.spec_gas_const,
bc_inflow=wing, bc_outflow=wing, bc_noslip=wing,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
discr = rcon.make_discretization(mesh_data, order=order,
debug=["cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code"
"cuda_no_metis",
],
default_scalar_type=numpy.float64,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = wing.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: 0.6 * op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("wing-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
from pyvisfile.silo import DB_VARTYPE_VECTOR
from hedge.discretization import ones_on_boundary
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
t += dt
finally:
vis.close()
logmgr.save()
discr.close()
def main(write_output=True):
from hedge.timestep.runge_kutta import LSRK4TimeStepper
from math import sqrt, pi, exp
from hedge.backends import guess_run_context
rcon = guess_run_context()
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
c = 1 / sqrt(mu * epsilon)
pml_width = 0.5
#mesh = make_mesh(a=np.array((-1,-1,-1)), b=np.array((1,1,1)),
#mesh = make_mesh(a=np.array((-3,-3)), b=np.array((3,3)),
mesh = make_mesh(
a=np.array((-1, -1)),
b=np.array((1, 1)),
#mesh = make_mesh(a=np.array((-2,-2)), b=np.array((2,2)),
pml_width=pml_width,
max_volume=0.01)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
class Current:
def volume_interpolant(self, t, discr):
from hedge.tools import make_obj_array
result = discr.volume_zeros(kind="numpy", dtype=np.float64)
omega = 6 * c
if omega * t > 2 * pi:
return make_obj_array([result, result, result])
x = make_obj_array(discr.nodes.T)
r = np.sqrt(np.dot(x, x))
idx = r < 0.3
result[idx] = (1+np.cos(pi*r/0.3))[idx] \
*np.sin(omega*t)**3
result = discr.convert_volume(result,
kind=discr.compute_kind,
dtype=discr.default_scalar_type)
return make_obj_array([-result, result, result])
order = 3
discr = rcon.make_discretization(mesh_data,
order=order,
debug=["cuda_no_plan"])
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.data import GivenFunction, TimeHarmonicGivenFunction, TimeIntervalGivenFunction
from hedge.models.em import MaxwellOperator
from hedge.models.pml import \
AbarbanelGottliebPMLMaxwellOperator, \
AbarbanelGottliebPMLTMMaxwellOperator, \
AbarbanelGottliebPMLTEMaxwellOperator
op = AbarbanelGottliebPMLTEMaxwellOperator(epsilon,
mu,
flux_type=1,
current=Current(),
pec_tag=TAG_ALL,
absorb_tag=TAG_NONE,
add_decay=True)
fields = op.assemble_ehpq(discr=discr)
stepper = LSRK4TimeStepper()
if rcon.is_head_rank:
print "order %d" % order
print "#elements=", len(mesh.elements)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "maxwell-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(
["step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max"])
from hedge.log import LpNorm
class FieldIdxGetter:
def __init__(self, whole_getter, idx):
self.whole_getter = whole_getter
self.idx = idx
def __call__(self):
return self.whole_getter()[self.idx]
# timestep loop -------------------------------------------------------
t = 0
pml_coeff = op.coefficients_from_width(discr, width=pml_width)
rhs = op.bind(discr, pml_coeff)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4 / c,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
e, h, p, q = op.split_ehpq(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
#pml_rhs_e, pml_rhs_h, pml_rhs_p, pml_rhs_q = \
#op.split_ehpq(rhs(t, fields))
j = Current().volume_interpolant(t, discr)
vis.add_data(
visf,
[
("e", discr.convert_volume(e, "numpy")),
("h", discr.convert_volume(h, "numpy")),
("p", discr.convert_volume(p, "numpy")),
("q", discr.convert_volume(q, "numpy")),
("j", discr.convert_volume(j, "numpy")),
#("pml_rhs_e", pml_rhs_e),
#("pml_rhs_h", pml_rhs_h),
#("pml_rhs_p", pml_rhs_p),
#("pml_rhs_q", pml_rhs_q),
#("max_rhs_e", max_rhs_e),
#("max_rhs_h", max_rhs_h),
#("max_rhs_p", max_rhs_p),
#("max_rhs_q", max_rhs_q),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
_, _, energies_data = logmgr.get_expr_dataset("W_el+W_mag")
energies = [value for tick_nbr, value in energies_data]
assert energies[-1] < max(energies) * 1e-2
finally:
logmgr.close()
if write_output:
vis.close()
def main(write_output=True):
from math import sin, cos, pi, exp, sqrt
from hedge.data import TimeConstantGivenFunction, \
ConstantGivenFunction
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
def boundary_tagger(fvi, el, fn, all_v):
if el.face_normals[fn][0] > 0:
return ["dirichlet"]
else:
return ["neumann"]
if dim == 2:
if rcon.is_head_rank:
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, boundary_tagger=boundary_tagger)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.001)
else:
raise RuntimeError, "bad number of dimensions"
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data,
order=3,
debug=["cuda_no_plan"],
default_scalar_type=numpy.float64)
if write_output:
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, rcon, "fld")
def u0(x, el):
if la.norm(x) < 0.2:
return 1
else:
return 0
def coeff(x, el):
if x[0] < 0:
return 0.25
else:
return 1
def dirichlet_bc(t, x):
return 0
def neumann_bc(t, x):
return 2
from hedge.models.diffusion import DiffusionOperator
op = DiffusionOperator(
discr.dimensions,
#coeff=coeff,
dirichlet_tag="dirichlet",
dirichlet_bc=TimeConstantGivenFunction(ConstantGivenFunction(0)),
neumann_tag="neumann",
neumann_bc=TimeConstantGivenFunction(ConstantGivenFunction(1)))
u = discr.interpolate_volume_function(u0)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "heat.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: u
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
from hedge.timestep.runge_kutta import LSRK4TimeStepper, ODE45TimeStepper
from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = LSRK4TimeStepper()
stepper = Dumka3TimeStepper(
3,
rtol=1e-6,
rcon=rcon,
vector_primitive_factory=discr.get_vector_primitive_factory(),
dtype=discr.default_scalar_type)
#stepper = ODE45TimeStepper(rtol=1e-6, rcon=rcon,
#vector_primitive_factory=discr.get_vector_primitive_factory(),
#dtype=discr.default_scalar_type)
stepper.add_instrumentation(logmgr)
rhs = op.bind(discr)
try:
next_dt = op.estimate_timestep(discr,
stepper=LSRK4TimeStepper(),
t=0,
fields=u)
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=0.1,
logmgr=logmgr,
max_dt_getter=lambda t: next_dt,
taken_dt_getter=lambda: taken_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(u, kind="numpy")),
],
time=t,
step=step)
visf.close()
u, t, taken_dt, next_dt = stepper(u, t, next_dt, rhs)
#u = stepper(u, t, dt, rhs)
assert discr.norm(u) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True,
flux_type_arg="central",
use_quadrature=True,
final_time=20):
from math import sin, cos, pi, sqrt
from hedge.backends import guess_run_context
rcon = guess_run_context()
# mesh setup --------------------------------------------------------------
if rcon.is_head_rank:
#from hedge.mesh.generator import make_disk_mesh
#mesh = make_disk_mesh()
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.008)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
# space-time-dependent-velocity-field -------------------------------------
# simple vortex
class TimeDependentVField:
""" `TimeDependentVField` is a callable expecting `(x, t)` representing space and time
`x` is of the length of the spatial dimension and `t` is the time."""
shape = (2, )
def __call__(self, pt, el, t):
x, y = pt
# Correction-Factor to make the speed zero on the on the boundary
#fac = (1-x**2)*(1-y**2)
fac = 1.
return numpy.array([-y * fac, x * fac]) * cos(pi * t)
class VField:
""" `VField` is a callable expecting `(x)` representing space
`x` is of the length of the spatial dimension."""
shape = (2, )
def __call__(self, pt, el):
x, y = pt
# Correction-Factor to make the speed zero on the on the boundary
#fac = (1-x**2)*(1-y**2)
fac = 1.
return numpy.array([-y * fac, x * fac])
# space-time-dependent State BC (optional)-----------------------------------
class TimeDependentBc_u:
""" space and time dependent BC for state u"""
def __call__(self, pt, el, t):
x, y = pt
if t <= 0.5:
if x > 0:
return 1
else:
return 0
else:
return 0
class Bc_u:
""" Only space dependent BC for state u"""
def __call__(seld, pt, el):
x, y = pt
if x > 0:
return 1
else:
return 0
# operator setup ----------------------------------------------------------
# In the operator setup it is possible to switch between a only space
# dependent velocity field `VField` or a time and space dependent
# `TimeDependentVField`.
# For `TimeDependentVField`: advec_v=TimeDependentGivenFunction(VField())
# For `VField`: advec_v=TimeConstantGivenFunction(GivenFunction(VField()))
# Same for the Bc_u Function! If you don't define Bc_u then the BC for u = 0.
from hedge.data import \
ConstantGivenFunction, \
TimeConstantGivenFunction, \
TimeDependentGivenFunction, \
GivenFunction
from hedge.models.advection import VariableCoefficientAdvectionOperator
op = VariableCoefficientAdvectionOperator(
mesh.dimensions,
#advec_v=TimeDependentGivenFunction(
# TimeDependentVField()),
advec_v=TimeConstantGivenFunction(GivenFunction(VField())),
#bc_u_f=TimeDependentGivenFunction(
# TimeDependentBc_u()),
bc_u_f=TimeConstantGivenFunction(GivenFunction(Bc_u())),
flux_type=flux_type_arg)
# discretization setup ----------------------------------------------------
order = 5
if use_quadrature:
quad_min_degrees = {"quad": 3 * order}
else:
quad_min_degrees = {}
discr = rcon.make_discretization(
mesh_data,
order=order,
default_scalar_type=numpy.float64,
debug=["cuda_no_plan"],
quad_min_degrees=quad_min_degrees,
tune_for=op.op_template(),
)
vis_discr = discr
# visualization setup -----------------------------------------------------
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(vis_discr, rcon, "fld")
# initial condition -------------------------------------------------------
if True:
def initial(pt, el):
# Gauss pulse
from math import exp
x = (pt - numpy.array([0.3, 0.5])) * 8
return exp(-numpy.dot(x, x))
else:
def initial(pt, el):
# Rectangle
x, y = pt
if abs(x) < 0.5 and abs(y) < 0.2:
return 2
else:
return 1
u = discr.interpolate_volume_function(initial)
# timestep setup ----------------------------------------------------------
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(
vector_primitive_factory=discr.get_vector_primitive_factory())
if rcon.is_head_rank:
print "%d elements" % len(discr.mesh.elements)
# filter setup-------------------------------------------------------------
from hedge.discretization import ExponentialFilterResponseFunction
from hedge.optemplate.operators import FilterOperator
mode_filter = FilterOperator(
ExponentialFilterResponseFunction(min_amplification=0.9,order=4))\
.bind(discr)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "space-dep.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from hedge.log import Integral, LpNorm
u_getter = lambda: u
logmgr.add_quantity(Integral(u_getter, discr, name="int_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, p=1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# Initialize v for data output:
v = op.advec_v.volume_interpolant(0, discr)
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[("u", discr.convert_volume(u, kind="numpy")),
("v", discr.convert_volume(v, kind="numpy"))],
time=t,
step=step)
visf.close()
u = stepper(u, t, dt, rhs)
# We're feeding in a discontinuity through the BCs.
# Quadrature does not help with shock capturing--
# therefore we do need to filter here, regardless
# of whether quadrature is enabled.
u = mode_filter(u)
assert discr.norm(u) < 10
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
final_time = 10
def u0(self, x):
return -sin(x + 0.3)
def main(
write_output=True,
flux_type_arg="upwind",
#case = CenteredStationaryTestCase(),
#case = OffCenterStationaryTestCase(),
#case = OffCenterMigratingTestCase(),
case=ExactTestCase(),
):
from hedge.backends import guess_run_context
rcon = guess_run_context()
order = 3
if rcon.is_head_rank:
if True:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(case.a, case.b, 20, periodic=True)
else:
from hedge.mesh.generator import make_rect_mesh
print(pi * 2) / (11 * 5 * 2)
mesh = make_rect_mesh((-pi, -1), (pi, 1),
periodicity=(True, True),
subdivisions=(11, 5),
max_area=(pi * 2) / (11 * 5 * 2))
if rcon.is_head_rank:
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(["cuda", "mpi"])
if rcon.is_head_rank:
mesh = make_wingmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
wing = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=wing.gamma,
mu=wing.mu,
prandtl=wing.prandtl,
spec_gas_const=wing.spec_gas_const,
bc_inflow=wing,
bc_outflow=wing,
bc_noslip=wing,
inflow_tag="inflow",
outflow_tag="outflow",
noslip_tag="noslip")
discr = rcon.make_discretization(
mesh_data,
order=order,
debug=[
"cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code"
"cuda_no_metis",
],
default_scalar_type=numpy.float64,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = wing.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w",
rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: 0.6 * op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("wing-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
from pyvisfile.silo import DB_VARTYPE_VECTOR
from hedge.discretization import ones_on_boundary
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
t += dt
finally:
vis.close()
logmgr.save()
discr.close()
def main(write_output=True, flux_type_arg="upwind",
#case = CenteredStationaryTestCase(),
#case = OffCenterStationaryTestCase(),
#case = OffCenterMigratingTestCase(),
case = ExactTestCase(),
):
from hedge.backends import guess_run_context
rcon = guess_run_context()
order = 3
if rcon.is_head_rank:
if True:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(case.a, case.b, 20, periodic=True)
else:
from hedge.mesh.generator import make_rect_mesh
print (pi*2)/(11*5*2)
mesh = make_rect_mesh((-pi, -1), (pi, 1),
periodicity=(True, True),
subdivisions=(11,5),
max_area=(pi*2)/(11*5*2)
)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=order,
quad_min_degrees={"quad": 3*order})
if write_output:
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, rcon, "fld")
# operator setup ----------------------------------------------------------
from hedge.second_order import IPDGSecondDerivative
from hedge.models.burgers import BurgersOperator
op = BurgersOperator(mesh.dimensions,
viscosity_scheme=IPDGSecondDerivative())
if rcon.is_head_rank:
print "%d elements" % len(discr.mesh.elements)
# exact solution ----------------------------------------------------------
import pymbolic
var = pymbolic.var
u = discr.interpolate_volume_function(lambda x, el: case.u0(x[0]))
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "burgers.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: u
logmgr.add_quantity(LpNorm(u_getter, discr, p=1, name="l1_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l1_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
from hedge.timestep.runge_kutta import ODE45TimeStepper, LSRK4TimeStepper
stepper = ODE45TimeStepper()
stepper.add_instrumentation(logmgr)
try:
from hedge.timestep import times_and_steps
# for visc=0.01
#stab_fac = 0.1 # RK4
#stab_fac = 1.6 # dumka3(3), central
#stab_fac = 3 # dumka3(4), central
#stab_fac = 0.01 # RK4
stab_fac = 0.2 # dumka3(3), central
#stab_fac = 3 # dumka3(4), central
dt = stab_fac*op.estimate_timestep(discr,
stepper=LSRK4TimeStepper(), t=0, fields=u)
step_it = times_and_steps(
final_time=case.final_time, logmgr=logmgr, max_dt_getter=lambda t: dt)
from hedge.optemplate import InverseVandermondeOperator
inv_vdm = InverseVandermondeOperator().bind(discr)
for step, t, dt in step_it:
if step % 3 == 0 and write_output:
if hasattr(case, "u_exact"):
extra_fields = [
("u_exact",
discr.interpolate_volume_function(
lambda x, el: case.u_exact(x[0], t)))]
else:
extra_fields = []
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", u),
] + extra_fields,
time=t,
step=step)
visf.close()
u = stepper(u, t, dt, rhs)
if isinstance(case, ExactTestCase):
assert discr.norm(u, 1) < 50
finally:
if write_output:
vis.close()
logmgr.save()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(["cuda"])
if rcon.is_head_rank:
mesh = make_boxmesh()
#from hedge.mesh import make_rect_mesh
#mesh = make_rect_mesh(
# boundary_tagger=lambda fvi, el, fn, all_v: ["inflow"])
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from gas_dynamics_initials import UniformMachFlow
box = UniformMachFlow(angle_of_attack=0)
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=3,
gamma=box.gamma, mu=box.mu,
prandtl=box.prandtl, spec_gas_const=box.spec_gas_const,
bc_inflow=box, bc_outflow=box, bc_noslip=box,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
discr = rcon.make_discretization(mesh_data, order=order,
debug=[
#"cuda_no_plan",
#"cuda_dump_kernels",
#"dump_dataflow_graph",
#"dump_optemplate_stages",
#"dump_dataflow_graph",
#"print_op_code",
"cuda_no_plan_el_local",
],
default_scalar_type=numpy.float32,
tune_for=op.op_template())
from hedge.visualization import SiloVisualizer, VtkVisualizer # noqa
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
fields = box.volume_interpolant(0, discr)
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
from pytools.log import LogQuantity
class ChangeSinceLastStep(LogQuantity):
"""Records the change of a variable between a time step and the previous
one"""
def __init__(self, name="change"):
LogQuantity.__init__(self, name, "1", "Change since last time step")
self.old_fields = 0
def __call__(self):
result = discr.norm(fields - self.old_fields)
self.old_fields = fields
return result
logmgr.add_quantity(ChangeSinceLastStep())
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=200,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 200 == 0:
#if False:
visf = vis.make_file("box-%d-%06d" % (order, step))
#rhs_fields = rhs(t, fields)
vis.add_data(visf,
[
("rho", discr.convert_volume(
op.rho(fields), kind="numpy")),
("e", discr.convert_volume(
op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(
op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(
op.u(fields), kind="numpy")),
# ("rhs_rho", discr.convert_volume(
# op.rho(rhs_fields), kind="numpy")),
# ("rhs_e", discr.convert_volume(
# op.e(rhs_fields), kind="numpy")),
# ("rhs_rho_u", discr.convert_volume(
# op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
("p", "(0.4)*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
finally:
vis.close()
logmgr.save()
discr.close()
def main(write_output=True):
from hedge.data import GivenFunction, ConstantGivenFunction
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
def boundary_tagger(fvi, el, fn, points):
from math import atan2, pi
normal = el.face_normals[fn]
if -90 / 180 * pi < atan2(normal[1], normal[0]) < 90 / 180 * pi:
return ["neumann"]
else:
return ["dirichlet"]
if dim == 2:
if rcon.is_head_rank:
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5,
boundary_tagger=boundary_tagger,
max_area=1e-2)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(
max_volume=0.0001,
boundary_tagger=lambda fvi, el, fn, points: ["dirichlet"])
else:
raise RuntimeError, "bad number of dimensions"
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=5, debug=[])
def dirichlet_bc(x, el):
from math import sin
return sin(10 * x[0])
def rhs_c(x, el):
if la.norm(x) < 0.1:
return 1000
else:
return 0
def my_diff_tensor():
result = numpy.eye(dim)
result[0, 0] = 0.1
return result
try:
from hedge.models.poisson import PoissonOperator
from hedge.second_order import \
IPDGSecondDerivative, LDGSecondDerivative, \
StabilizedCentralSecondDerivative
from hedge.mesh import TAG_NONE, TAG_ALL
op = PoissonOperator(
discr.dimensions,
diffusion_tensor=my_diff_tensor(),
#dirichlet_tag="dirichlet",
#neumann_tag="neumann",
dirichlet_tag=TAG_ALL,
neumann_tag=TAG_NONE,
#dirichlet_tag=TAG_ALL,
#neumann_tag=TAG_NONE,
dirichlet_bc=GivenFunction(dirichlet_bc),
neumann_bc=ConstantGivenFunction(-10),
scheme=StabilizedCentralSecondDerivative(),
#scheme=LDGSecondDerivative(),
#scheme=IPDGSecondDerivative(),
)
bound_op = op.bind(discr)
from hedge.iterative import parallel_cg
u = -parallel_cg(rcon,
-bound_op,
bound_op.prepare_rhs(
discr.interpolate_volume_function(rhs_c)),
debug=20,
tol=5e-4,
dot=discr.nodewise_dot_product,
x=discr.volume_zeros())
if write_output:
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon)
visf = vis.make_file("fld")
vis.add_data(visf, [
("sol", discr.convert_volume(u, kind="numpy")),
])
visf.close()
finally:
discr.close()
def main(write_output=True):
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import EOCRecorder
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from hedge.mesh.generator import \
make_rect_mesh, \
make_centered_regular_rect_mesh
refine = 4
mesh = make_centered_regular_rect_mesh((0, -5), (10, 5),
n=(9, 9),
post_refine_factor=refine)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3, 4, 5]:
from gas_dynamics_initials import Vortex
flow = Vortex()
from hedge.models.gas_dynamics import (GasDynamicsOperator,
PolytropeEOS, GammaLawEOS)
from hedge.mesh import TAG_ALL
# works equally well for GammaLawEOS
op = GasDynamicsOperator(dimensions=2,
mu=flow.mu,
prandtl=flow.prandtl,
spec_gas_const=flow.spec_gas_const,
equation_of_state=PolytropeEOS(flow.gamma),
bc_inflow=flow,
bc_outflow=flow,
bc_noslip=flow,
inflow_tag=TAG_ALL,
source=None)
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=numpy.float64,
quad_min_degrees={
"gasdyn_vol": 3 * order,
"gasdyn_face": 3 * order,
},
tune_for=op.op_template(),
debug=["cuda_no_plan"])
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "vortex-%d" % order)
#vis = SiloVisualizer(discr, rcon)
fields = flow.volume_interpolant(0, discr)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
# limiter ------------------------------------------------------------
from hedge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, flow.gamma, 2, op)
from hedge.timestep.runge_kutta import SSP3TimeStepper
#stepper = SSP3TimeStepper(limiter=limiter)
stepper = SSP3TimeStepper(
vector_primitive_factory=discr.get_vector_primitive_factory())
#from hedge.timestep import RK4TimeStepper
#stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "euler-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
final_time = flow.final_time
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
print "run until t=%g" % final_time
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
#true_fields = vortex.volume_interpolant(t, discr)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
#expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
#("p", "0.4*(e- 0.5*(rho_u*u))"),
#],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
#fields = limiter(fields)
assert not numpy.isnan(numpy.sum(fields[0]))
true_fields = flow.volume_interpolant(final_time, discr)
l2_error = discr.norm(fields - true_fields)
l2_error_rho = discr.norm(op.rho(fields) - op.rho(true_fields))
l2_error_e = discr.norm(op.e(fields) - op.e(true_fields))
l2_error_rhou = discr.norm(
op.rho_u(fields) - op.rho_u(true_fields))
l2_error_u = discr.norm(op.u(fields) - op.u(true_fields))
eoc_rec.add_data_point(order, l2_error)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
logmgr.set_constant("l2_error_rho", l2_error_rho)
logmgr.set_constant("l2_error_e", l2_error_e)
logmgr.set_constant("l2_error_rhou", l2_error_rhou)
logmgr.set_constant("l2_error_u", l2_error_u)
logmgr.set_constant("refinement", refine)
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
# after order loop
assert eoc_rec.estimate_order_of_convergence()[0, 1] > 6
def main(write_output=True,
flux_type_arg="upwind", dtype=numpy.float64, debug=[]):
from pytools.stopwatch import Job
from math import sin, cos, pi, exp, sqrt
from hedge.backends import guess_run_context
rcon = guess_run_context()
if rcon.is_head_rank:
from hedge.mesh.reader.gmsh import generate_gmsh
mesh = generate_gmsh(GEOMETRY, 2,
allow_internal_boundaries=True)
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=4, debug=debug,
default_scalar_type=dtype)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper(dtype=dtype)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
def source_u(x, el):
return exp(-numpy.dot(x, x)*128)
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE
from hedge.data import \
make_tdep_given, \
TimeHarmonicGivenFunction, \
TimeIntervalGivenFunction
op = StrongWaveOperator(-1, discr.dimensions,
source_f=TimeIntervalGivenFunction(
TimeHarmonicGivenFunction(
make_tdep_given(source_u), omega=10),
0, 1),
dirichlet_tag="boundary",
neumann_tag=TAG_NONE,
radiation_tag=TAG_NONE,
flux_type=flux_type_arg
)
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(dtype=dtype),
[discr.volume_zeros(dtype=dtype) for i in range(discr.dimensions)])
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wiggly.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
assert fields[0].dtype == dtype
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True,
dir_tag=TAG_NONE,
neu_tag=TAG_NONE,
rad_tag=TAG_ALL,
flux_type_arg="upwind"):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.003)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=4)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
source_center = np.array([0.7, 0.4])
source_width = 1 / 16
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import VariableVelocityStrongWaveOperator
op = VariableVelocityStrongWaveOperator(
c=sym.If(sym.Comparison(np.dot(sym_x, sym_x), "<", 0.4**2), 1, 0.5),
dimensions=discr.dimensions,
source=sym.CFunction("sin")(source_omega * sym.ScalarParameter("t")) *
sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg)
from hedge.tools import join_fields
fields = join_fields(
discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep.stability import \
approximate_rk4_relative_imag_stability_region
max_dt = (1 / discr.compile(op.max_eigenvalue_expr())() *
discr.dt_non_geometric_factor() *
discr.dt_geometric_factor() *
approximate_rk4_relative_imag_stability_region(stepper))
if flux_type_arg == "central":
max_dt *= 0.25
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=3,
logmgr=logmgr,
max_dt_getter=lambda t: max_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True,
flux_type_arg="upwind",
dtype=np.float64,
debug=[]):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
if rcon.is_head_rank:
from hedge.mesh.reader.gmsh import generate_gmsh
mesh = generate_gmsh(GEOMETRY,
2,
allow_internal_boundaries=True,
force_dimension=2)
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data,
order=4,
debug=debug,
default_scalar_type=dtype)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=dtype)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
source_center = 0
source_width = 0.05
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import StrongWaveOperator
op = StrongWaveOperator(
-1,
discr.dimensions,
source_f=sym.CFunction("sin")(
source_omega * sym.ScalarParameter("t")) * sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2),
dirichlet_tag="boundary",
neumann_tag=TAG_NONE,
radiation_tag=TAG_NONE,
flux_type=flux_type_arg)
from hedge.tools import join_fields
fields = join_fields(
discr.volume_zeros(dtype=dtype),
[discr.volume_zeros(dtype=dtype) for i in range(discr.dimensions)])
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wiggly.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -----------------------------------------------------------
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
assert fields[0].dtype == dtype
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True, allow_features=None, flux_type_arg=1, bdry_flux_type_arg=None, extra_discr_args={}):
from hedge.mesh.generator import make_cylinder_mesh, make_box_mesh
from hedge.tools import EOCRecorder, to_obj_array
from math import sqrt, pi
from analytic_solutions import (
check_time_harmonic_solution,
RealPartAdapter,
SplitComplexAdapter,
CylindricalFieldAdapter,
CylindricalCavityMode,
RectangularWaveguideMode,
RectangularCavityMode,
)
from hedge.models.em import MaxwellOperator
from hedge.backends import guess_run_context
rcon = guess_run_context(allow_features)
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
eoc_rec = EOCRecorder()
cylindrical = False
periodic = False
if cylindrical:
R = 1
d = 2
mode = CylindricalCavityMode(m=1, n=1, p=1, radius=R, height=d, epsilon=epsilon, mu=mu)
r_sol = CylindricalFieldAdapter(RealPartAdapter(mode))
c_sol = SplitComplexAdapter(CylindricalFieldAdapter(mode))
if rcon.is_head_rank:
mesh = make_cylinder_mesh(radius=R, height=d, max_volume=0.01)
else:
if periodic:
mode = RectangularWaveguideMode(epsilon, mu, (3, 2, 1))
periodicity = (False, False, True)
else:
periodicity = None
mode = RectangularCavityMode(epsilon, mu, (1, 2, 2))
if rcon.is_head_rank:
mesh = make_box_mesh(max_volume=0.001, periodicity=periodicity)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [4, 5, 6]:
# for order in [1,2,3,4,5,6]:
extra_discr_args.setdefault("debug", []).extend(["cuda_no_plan", "cuda_dump_kernels"])
op = MaxwellOperator(epsilon, mu, flux_type=flux_type_arg, bdry_flux_type=bdry_flux_type_arg)
discr = rcon.make_discretization(mesh_data, order=order, tune_for=op.op_template(), **extra_discr_args)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "em-%d" % order)
mode.set_time(0)
def get_true_field():
return discr.convert_volume(
to_obj_array(mode(discr).real.astype(discr.default_scalar_type).copy()), kind=discr.compute_kind
)
fields = get_true_field()
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type, rcon=rcon)
# from hedge.timestep.dumka3 import Dumka3TimeStepper
# stepper = Dumka3TimeStepper(3, dtype=discr.default_scalar_type, rcon=rcon)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, add_simulation_quantities, add_run_info
if write_output:
log_file_name = "maxwell-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(["step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max"])
# timestep loop -------------------------------------------------------
rhs = op.bind(discr)
final_time = 0.5e-9
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr, stepper=stepper, t=t, fields=fields),
)
for step, t, dt in step_it:
if step % 50 == 0 and write_output:
sub_timer = vis_timer.start_sub_timer()
e, h = op.split_eh(fields)
visf = vis.make_file("em-%d-%04d" % (order, step))
vis.add_data(
visf,
[("e", discr.convert_volume(e, kind="numpy")), ("h", discr.convert_volume(h, kind="numpy"))],
time=t,
step=step,
)
visf.close()
sub_timer.stop().submit()
fields = stepper(fields, t, dt, rhs)
mode.set_time(final_time)
eoc_rec.add_data_point(order, discr.norm(fields - get_true_field()))
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
if rcon.is_head_rank:
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
assert eoc_rec.estimate_order_of_convergence()[0, 1] > 6
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context(
#["cuda"]
)
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
def boundary_tagger(vertices, el, face_nr, all_v):
return ["inflow"]
if rcon.is_head_rank:
from hedge.mesh import make_rect_mesh, \
make_centered_regular_rect_mesh
#mesh = make_rect_mesh((0,0), (10,1), max_area=0.01)
refine = 1
mesh = make_centered_regular_rect_mesh((0,0), (10,1), n=(20,4),
#periodicity=(True, False),
post_refine_factor=refine,
boundary_tagger=boundary_tagger)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3]:
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "shearflow-%d" % order)
vis = SiloVisualizer(discr, rcon)
shearflow = SteadyShearFlow()
fields = shearflow.volume_interpolant(0, discr)
gamma, mu, prandtl, spec_gas_const = shearflow.properties()
from hedge.models.gas_dynamics import GasDynamicsOperator
op = GasDynamicsOperator(dimensions=2, gamma=gamma, mu=mu,
prandtl=prandtl, spec_gas_const=spec_gas_const,
bc_inflow=shearflow, bc_outflow=shearflow, bc_noslip=shearflow,
inflow_tag="inflow", outflow_tag="outflow", noslip_tag="noslip")
navierstokes_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = navierstokes_ex(t, q)
max_eigval[0] = speed
return ode_rhs
# needed to get first estimate of maximum eigenvalue
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("navierstokes-cpu-%d-%d.dat" % (order, refine),
"w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=0.3,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 10 == 0:
#if False:
visf = vis.make_file("shearflow-%d-%04d" % (order, step))
#true_fields = shearflow.volume_interpolant(t, discr)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
],
expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "0.4*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
true_fields = shearflow.volume_interpolant(t, discr)
l2_error = discr.norm(op.u(fields)-op.u(true_fields))
eoc_rec.add_data_point(order, l2_error)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
finally:
vis.close()
logmgr.save()
discr.close()
def main(write_output=True):
from hedge.data import GivenFunction, ConstantGivenFunction
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
def boundary_tagger(fvi, el, fn, points):
from math import atan2, pi
normal = el.face_normals[fn]
if -90/180*pi < atan2(normal[1], normal[0]) < 90/180*pi:
return ["neumann"]
else:
return ["dirichlet"]
if dim == 2:
if rcon.is_head_rank:
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, boundary_tagger=boundary_tagger,
max_area=1e-2)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0001,
boundary_tagger=lambda fvi, el, fn, points:
["dirichlet"])
else:
raise RuntimeError, "bad number of dimensions"
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=5,
debug=[])
def dirichlet_bc(x, el):
from math import sin
return sin(10*x[0])
def rhs_c(x, el):
if la.norm(x) < 0.1:
return 1000
else:
return 0
def my_diff_tensor():
result = numpy.eye(dim)
result[0,0] = 0.1
return result
try:
from hedge.models.poisson import PoissonOperator
from hedge.second_order import \
IPDGSecondDerivative, LDGSecondDerivative, \
StabilizedCentralSecondDerivative
from hedge.mesh import TAG_NONE, TAG_ALL
op = PoissonOperator(discr.dimensions,
diffusion_tensor=my_diff_tensor(),
#dirichlet_tag="dirichlet",
#neumann_tag="neumann",
dirichlet_tag=TAG_ALL,
neumann_tag=TAG_NONE,
#dirichlet_tag=TAG_ALL,
#neumann_tag=TAG_NONE,
dirichlet_bc=GivenFunction(dirichlet_bc),
neumann_bc=ConstantGivenFunction(-10),
scheme=StabilizedCentralSecondDerivative(),
#scheme=LDGSecondDerivative(),
#scheme=IPDGSecondDerivative(),
)
bound_op = op.bind(discr)
from hedge.iterative import parallel_cg
u = -parallel_cg(rcon, -bound_op,
bound_op.prepare_rhs(discr.interpolate_volume_function(rhs_c)),
debug=20, tol=5e-4,
dot=discr.nodewise_dot_product,
x=discr.volume_zeros())
if write_output:
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon)
visf = vis.make_file("fld")
vis.add_data(visf, [ ("sol", discr.convert_volume(u, kind="numpy")), ])
visf.close()
finally:
discr.close()
def main(write_output=True, allow_features=None):
from hedge.timestep import RK4TimeStepper
from hedge.mesh import make_ball_mesh, make_cylinder_mesh, make_box_mesh
from hedge.visualization import \
VtkVisualizer, \
SiloVisualizer, \
get_rank_partition
from math import sqrt, pi
from hedge.backends import guess_run_context
rcon = guess_run_context(allow_features)
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
dims = 3
if rcon.is_head_rank:
if dims == 2:
from hedge.mesh import make_rect_mesh
mesh = make_rect_mesh(a=(-10.5, -1.5), b=(10.5, 1.5), max_area=0.1)
elif dims == 3:
from hedge.mesh import make_box_mesh
mesh = make_box_mesh(a=(-10.5, -1.5, -1.5),
b=(10.5, 1.5, 1.5),
max_volume=0.1)
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
#for order in [1,2,3,4,5,6]:
discr = rcon.make_discretization(mesh_data, order=3)
if write_output:
vis = VtkVisualizer(discr, rcon, "dipole")
from analytic_solutions import DipoleFarField, SphericalFieldAdapter
from hedge.data import ITimeDependentGivenFunction
sph_dipole = DipoleFarField(
q=1, #C
d=1 / 39,
omega=2 * pi * 1e8,
epsilon=epsilon0,
mu=mu0,
)
cart_dipole = SphericalFieldAdapter(sph_dipole)
class PointDipoleSource(ITimeDependentGivenFunction):
def __init__(self):
from pyrticle.tools import CInfinityShapeFunction
sf = CInfinityShapeFunction(0.1 * sph_dipole.wavelength,
discr.dimensions)
self.num_sf = discr.interpolate_volume_function(
lambda x, el: sf(x))
self.vol_0 = discr.volume_zeros()
def volume_interpolant(self, t, discr):
from hedge.tools import make_obj_array
return make_obj_array([
self.vol_0, self.vol_0,
sph_dipole.source_modulation(t) * self.num_sf
])
from hedge.mesh import TAG_ALL, TAG_NONE
if dims == 2:
from hedge.models.em import TMMaxwellOperator as MaxwellOperator
else:
from hedge.models.em import MaxwellOperator
op = MaxwellOperator(
epsilon,
mu,
flux_type=1,
pec_tag=TAG_NONE,
absorb_tag=TAG_ALL,
current=PointDipoleSource(),
)
fields = op.assemble_eh(discr=discr)
if rcon.is_head_rank:
print "#elements=", len(mesh.elements)
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "dipole.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
from hedge.log import EMFieldGetter, add_em_quantities
field_getter = EMFieldGetter(discr, op, lambda: fields)
add_em_quantities(logmgr, op, field_getter)
from pytools.log import PushLogQuantity
relerr_e_q = PushLogQuantity("relerr_e", "1",
"Relative error in masked E-field")
relerr_h_q = PushLogQuantity("relerr_h", "1",
"Relative error in masked H-field")
logmgr.add_quantity(relerr_e_q)
logmgr.add_quantity(relerr_h_q)
logmgr.add_watches([
"step.max", "t_sim.max", ("W_field", "W_el+W_mag"), "t_step.max",
"relerr_e", "relerr_h"
])
if write_output:
point_timeseries = [(open("b-x%d-vs-time.dat" % i,
"w"), open("b-x%d-vs-time-true.dat" % i,
"w"),
discr.get_point_evaluator(
numpy.array([i, 0, 0][:dims],
dtype=discr.default_scalar_type)))
for i in range(1, 5)]
# timestep loop -------------------------------------------------------
mask = discr.interpolate_volume_function(sph_dipole.far_field_mask)
def apply_mask(field):
from hedge.tools import log_shape
ls = log_shape(field)
result = discr.volume_empty(ls)
from pytools import indices_in_shape
for i in indices_in_shape(ls):
result[i] = mask * field[i]
return result
rhs = op.bind(discr)
t = 0
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1e-8,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if write_output and step % 10 == 0:
sub_timer = vis_timer.start_sub_timer()
e, h = op.split_eh(fields)
sph_dipole.set_time(t)
true_e, true_h = op.split_eh(
discr.interpolate_volume_function(cart_dipole))
visf = vis.make_file("dipole-%04d" % step)
mask_e = apply_mask(e)
mask_h = apply_mask(h)
mask_true_e = apply_mask(true_e)
mask_true_h = apply_mask(true_h)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf, [("e", e), ("h", h), ("true_e", true_e),
("true_h", true_h), ("mask_e", mask_e),
("mask_h", mask_h),
("mask_true_e", mask_true_e),
("mask_true_h", mask_true_h)],
time=t,
step=step)
visf.close()
sub_timer.stop().submit()
from hedge.tools import relative_error
relerr_e_q.push_value(
relative_error(discr.norm(mask_e - mask_true_e),
discr.norm(mask_true_e)))
relerr_h_q.push_value(
relative_error(discr.norm(mask_h - mask_true_h),
discr.norm(mask_true_h)))
if write_output:
for outf_num, outf_true, evaluator in point_timeseries:
for outf, ev_h in zip([outf_num, outf_true],
[h, true_h]):
outf.write("%g\t%g\n" %
(t, op.mu * evaluator(ev_h[1])))
outf.flush()
fields = stepper(fields, t, dt, rhs)
finally:
if write_output:
vis.close()
logmgr.save()
discr.close()
def run_convergence_test_advec(dtype,
flux_type,
random_partition,
mesh_gen,
debug_output=False):
"""Test whether 2/3D advection actually converges"""
from hedge.timestep import RK4TimeStepper
from hedge.tools import EOCRecorder
from math import sin
from hedge.data import TimeDependentGivenFunction
from hedge.visualization import SiloVisualizer
from hedge.backends import guess_run_context
rcon = guess_run_context(["mpi"])
# note: x component must remain zero because x-periodicity is used
v = np.array([0.0, 0.9, 0.3])
def f(x):
return sin(x)
def u_analytic(x, el, t):
return f(
(np.dot(-v[:dims], x) / la.norm(v[:dims]) + t * la.norm(v[:dims])))
def boundary_tagger(vertices, el, face_nr, points):
face_normal = el.face_normals[face_nr]
if np.dot(face_normal, v[:len(face_normal)]) < 0:
return ["inflow"]
else:
return ["outflow"]
mesh = mesh_gen(boundary_tagger)
eoc_rec = EOCRecorder()
if random_partition:
# Distribute elements randomly across nodes.
# This is bad, efficiency-wise, but it puts stress
# on the parallel implementation, which is desired here.
# Another main point of this is to force the code to split
# a periodic face pair across nodes.
from random import choice
partition = [choice(rcon.ranks) for el in mesh.elements]
else:
partition = None
for order in [1, 2, 3, 4]:
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh, partition)
else:
mesh_data = rcon.receive_mesh()
dims = mesh.points.shape[1]
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=dtype)
op = StrongAdvectionOperator(
v[:dims],
inflow_u=TimeDependentGivenFunction(u_analytic),
flux_type=flux_type)
if debug_output:
vis = SiloVisualizer(discr, rcon)
u = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, 0))
ic = u.copy()
if debug_output and rcon.is_head_rank:
print "#elements=%d" % len(mesh.elements)
test_name = "test-%s-o%d-m%s-r%s" % (
flux_type, order, mesh_gen.__name__, random_partition)
rhs = op.bind(discr)
stepper = RK4TimeStepper(dtype=dtype)
from hedge.timestep import times_and_steps
final_time = 1
step_it = times_and_steps(final_time=final_time,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
u = stepper(u, t, dt, rhs)
assert u.dtype == dtype
u_true = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, final_time))
error = u - u_true
l2_error = discr.norm(error)
if debug_output:
visf = vis.make_file(test_name + "-final")
vis.add_data(visf, [("u", u), ("u_true", u_true), ("ic", ic)])
visf.close()
eoc_rec.add_data_point(order, l2_error)
if debug_output and rcon.is_head_rank:
print "%s\n%s\n" % (flux_type.upper(), "-" * len(flux_type))
print eoc_rec.pretty_print(abscissa_label="Poly. Order",
error_label="L2 Error")
assert eoc_rec.estimate_order_of_convergence()[0, 1] > 3
assert eoc_rec.estimate_order_of_convergence(2)[-1, 1] > 7
def main(write_output=True, allow_features=None, flux_type_arg=1,
bdry_flux_type_arg=None, extra_discr_args={}):
from math import sqrt, pi
from hedge.models.em import TEMaxwellOperator
from hedge.backends import guess_run_context
rcon = guess_run_context(allow_features)
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4*pi*1e-7 # N/A**2.
c = 1/sqrt(mu0*epsilon0)
materials = {"vacuum" : (epsilon0, mu0),
"dielectric" : (2*epsilon0, mu0)}
output_dir = "2d_cavity"
import os
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
# should no tag raise an error or default to free space?
def eps_val(x, el):
for key in materials.keys():
if el in material_elements[key]:
return materials[key][0]
raise ValueError, "Element does not belong to any material"
def mu_val(x, el):
for key in materials.keys():
if el in material_elements[key]:
return materials[key][1]
raise ValueError, "Element does not belong to any material"
# geometry of cavity
d = 100e-3
a = 150e-3
# analytical frequency and transverse wavenumbers of resonance
f0 = 9.0335649907522321e8
h = 2*pi*f0/c
l = -h*sqrt(2)
# substitute the following and change materials for a homogeneous cavity
#h = pi/a
#l =-h
def initial_val(discr):
# the initial solution for the TE_10-like mode
def initial_Hz(x, el):
from math import cos, sin
if el in material_elements["vacuum"]:
return h*cos(h*x[0])
else:
return -l*sin(h*d)/sin(l*(a-d))*cos(l*(a-x[0]))
from hedge.tools import make_obj_array
result_zero = discr.volume_zeros(kind="numpy", dtype=numpy.float64)
H_z = make_tdep_given(initial_Hz).volume_interpolant(0, discr)
return make_obj_array([result_zero, result_zero, H_z])
if rcon.is_head_rank:
from hedge.mesh.reader.gmsh import generate_gmsh
mesh = generate_gmsh(CAVITY_GEOMETRY, 2, force_dimension=2)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
# Work out which elements belong to each material
material_elements = {}
for key in materials.keys():
material_elements[key] = set(mesh_data.tag_to_elements[key])
order = 3
#extra_discr_args.setdefault("debug", []).append("cuda_no_plan")
#extra_discr_args.setdefault("debug", []).append("dump_optemplate_stages")
from hedge.data import make_tdep_given
from hedge.mesh import TAG_ALL
op = TEMaxwellOperator(epsilon=make_tdep_given(eps_val), mu=make_tdep_given(mu_val), \
flux_type=flux_type_arg, \
bdry_flux_type=bdry_flux_type_arg, dimensions=2, pec_tag=TAG_ALL)
# op = TEMaxwellOperator(epsilon=epsilon0, mu=mu0,
# flux_type=flux_type_arg, \
# bdry_flux_type=bdry_flux_type_arg, dimensions=2, pec_tag=TAG_ALL)
discr = rcon.make_discretization(mesh_data, order=order,
tune_for=op.op_template(),
**extra_discr_args)
# create the initial solution
fields = initial_val(discr)
from hedge.visualization import VtkVisualizer
if write_output:
from os.path import join
vis = VtkVisualizer(discr, rcon, join(output_dir, "cav-%d" % order))
# monitor the solution at a point to find the resonant frequency
try:
point_getter = discr.get_point_evaluator(numpy.array([75e-3, 25e-3, 0])) #[0.25, 0.25, 0.25]))
except RuntimeError:
point_getter = None
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=discr.default_scalar_type, rcon=rcon)
#from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = Dumka3TimeStepper(3, dtype=discr.default_scalar_type, rcon=rcon)
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
from os.path import join
log_file_name = join(output_dir, "cavity-%d.dat" % order)
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
#from hedge.log import EMFieldGetter, add_em_quantities
#field_getter = EMFieldGetter(discr, op, lambda: fields)
#add_em_quantities(logmgr, op, field_getter)
logmgr.add_watches(
["step.max", "t_sim.max",
#("W_field", "W_el+W_mag"),
"t_step.max"]
)
# timestep loop -------------------------------------------------------
rhs = op.bind(discr)
final_time = 10e-9
if point_getter is not None:
from os.path import join
pointfile = open(join(output_dir, "point.txt"), "wt")
done_dt = False
try:
from hedge.timestep import times_and_steps
from os.path import join
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
sub_timer = vis_timer.start_sub_timer()
e, h = op.split_eh(fields)
visf = vis.make_file(join(output_dir, "cav-%d-%04d") % (order, step))
vis.add_data(visf,
[
("e",
discr.convert_volume(e, kind="numpy")),
("h",
discr.convert_volume(h, kind="numpy")),],
time=t, step=step
)
visf.close()
sub_timer.stop().submit()
fields = stepper(fields, t, dt, rhs)
if point_getter is not None:
val = point_getter(fields)
#print val
if not done_dt:
pointfile.write("#%g\n" % dt)
done_dt = True
pointfile.write("%g\n" %val[0])
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
if point_getter is not None:
pointfile.close()
def main(write_output=True,
dir_tag=TAG_NONE,
neu_tag=TAG_NONE,
rad_tag=TAG_ALL,
flux_type_arg="upwind"):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.003)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=4)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
source_center = np.array([0.7, 0.4])
source_width = 1/16
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import VariableVelocityStrongWaveOperator
op = VariableVelocityStrongWaveOperator(
c=sym.If(sym.Comparison(
np.dot(sym_x, sym_x), "<", 0.4**2),
1, 0.5),
dimensions=discr.dimensions,
source=
sym.CFunction("sin")(source_omega*sym.ScalarParameter("t"))
* sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg
)
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep.stability import \
approximate_rk4_relative_imag_stability_region
max_dt = (
1/discr.compile(op.max_eigenvalue_expr())()
* discr.dt_non_geometric_factor()
* discr.dt_geometric_factor()
* approximate_rk4_relative_imag_stability_region(stepper))
if flux_type_arg == "central":
max_dt *= 0.25
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=3, logmgr=logmgr,
max_dt_getter=lambda t: max_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import to_obj_array
if rcon.is_head_rank:
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh((-5, -5), (5, 5), max_area=0.01)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [1]:
discr = rcon.make_discretization(mesh_data, order=order, default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "Sod2D-%d" % order)
# vis = SiloVisualizer(discr, rcon)
sod_field = Sod(gamma=1.4)
fields = sod_field.volume_interpolant(0, discr)
from hedge.models.gas_dynamics import GasDynamicsOperator
from hedge.mesh import TAG_ALL
op = GasDynamicsOperator(
dimensions=2,
gamma=sod_field.gamma,
mu=0.0,
prandtl=sod_field.prandtl,
bc_inflow=sod_field,
bc_outflow=sod_field,
bc_noslip=sod_field,
inflow_tag=TAG_ALL,
source=None,
)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
# limiter setup ------------------------------------------------------------
from hedge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, sod_field.gamma, 2, op)
# integrator setup---------------------------------------------------------
from hedge.timestep import SSPRK3TimeStepper, RK4TimeStepper
stepper = SSPRK3TimeStepper(limiter=limiter)
# stepper = SSPRK3TimeStepper()
# stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, add_simulation_quantities, add_run_info
logmgr = LogManager("euler-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# filter setup-------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(discr, ExponentialFilterResponseFunction(min_amplification=0.9, order=4))
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1.0,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]),
)
for step, t, dt in step_it:
if step % 5 == 0:
# if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
# true_fields = vortex.volume_interpolant(t, discr)
# from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(
visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
# ("true_rho", op.rho(true_fields)),
# ("true_e", op.e(true_fields)),
# ("true_rho_u", op.rho_u(true_fields)),
# ("true_u", op.u(true_fields)),
# ("rhs_rho", op.rho(rhs_fields)),
# ("rhs_e", op.e(rhs_fields)),
# ("rhs_rho_u", op.rho_u(rhs_fields)),
],
# expressions=[
# ("diff_rho", "rho-true_rho"),
# ("diff_e", "e-true_e"),
# ("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
# ("p", "0.4*(e- 0.5*(rho_u*u))"),
# ],
time=t,
step=step,
)
visf.close()
fields = stepper(fields, t, dt, rhs)
# fields = limiter(fields)
# fields = mode_filter(fields)
assert not numpy.isnan(numpy.sum(fields[0]))
finally:
vis.close()
logmgr.close()
discr.close()
# not solution, just to check against when making code changes
true_fields = sod_field.volume_interpolant(t, discr)
print discr.norm(fields - true_fields)
def test_kv_with_no_charge():
from random import seed
seed(0)
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
# discretization setup ----------------------------------------------------
from hedge.mesh import make_cylinder_mesh
from hedge.backends import guess_run_context
rcon = guess_run_context([])
tube_length = 100*units.MM
mesh = make_cylinder_mesh(radius=25*units.MM, height=tube_length, periodic=True)
discr = rcon.make_discretization(mesh, order=3)
dt = discr.dt_factor(units.VACUUM_LIGHT_SPEED()) / 2
final_time = 1*units.M/units.VACUUM_LIGHT_SPEED()
nsteps = int(final_time/dt)+1
dt = final_time/nsteps
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units,
ShapeFunctionDepositor(),
MonomialParticlePusher(),
3, 3)
nparticles = 10000
cloud_charge = 1e-9 * units.C
electrons_per_particle = cloud_charge/nparticles/units.EL_CHARGE
el_energy = 5.2e6 * units.EV
gamma = el_energy/units.EL_REST_ENERGY()
beta = (1-1/gamma**2)**0.5
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units,
total_charge=0,
p_charge=0,
p_mass=electrons_per_particle*units.EL_MASS,
radii=2*[2.5*units.MM],
emittances=2*[5 * units.MM * units.MRAD],
z_length=5*units.MM,
z_pos=10*units.MM,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager
from pyrticle.log import add_beam_quantities, StateObserver
observer = StateObserver(method, None)
logmgr = LogManager(mode="w")
add_beam_quantities(logmgr, observer, axis=0, beam_axis=2)
from pyrticle.distribution import KVPredictedRadius
logmgr.add_quantity(KVPredictedRadius(dt,
beam_v=beta*units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_rms_predictor(axis=0),
suffix="x_rms"))
logmgr.add_quantity(KVPredictedRadius(dt,
beam_v=beta*units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_total_predictor(axis=0),
suffix="x_total"))
# timestep loop -----------------------------------------------------------
vel = method.velocities(state)
from hedge.tools import join_fields
def rhs(t, y):
return join_fields([
vel,
0*vel,
0, # drecon
])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
t = 0
from pyrticle.cloud import TimesteppablePicState
ts_state = TimesteppablePicState(method, state)
for step in xrange(nsteps):
observer.set_fields_and_state(None, ts_state.state)
logmgr.tick()
ts_state = stepper(ts_state, t, dt, rhs)
method.upkeep(ts_state.state)
t += dt
logmgr.tick()
_, _, err_table = logmgr.get_expr_dataset("(rx_rms-rx_rms_theory)/rx_rms_theory")
rel_max_rms_error = max(err for step, err in err_table)
assert rel_max_rms_error < 0.01
def main(write_output=True,
dir_tag=TAG_NONE,
neu_tag=TAG_NONE,
rad_tag=TAG_ALL,
flux_type_arg="upwind",
dtype=np.float64,
debug=[]):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=dtype)
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE # noqa
source_center = np.array([0.1, 0.22])
source_width = 0.05
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
op = StrongWaveOperator(
-1,
dim,
source_f=sym.CFunction("sin")(
source_omega * sym.ScalarParameter("t")) * sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg)
discr = rcon.make_discretization(mesh_data,
order=4,
debug=debug,
default_scalar_type=dtype,
tune_for=op.op_template())
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.tools import join_fields
fields = join_fields(
discr.volume_zeros(dtype=dtype),
[discr.volume_zeros(dtype=dtype) for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=4,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(fields[0], kind="numpy")),
("v", discr.convert_volume(fields[1:], kind="numpy")),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
assert fields[0].dtype == dtype
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True):
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import EOCRecorder
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from hedge.mesh.generator import \
make_rect_mesh, \
make_centered_regular_rect_mesh
refine = 4
mesh = make_centered_regular_rect_mesh((0,-5), (10,5), n=(9,9),
post_refine_factor=refine)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [3, 4, 5]:
from gas_dynamics_initials import Vortex
flow = Vortex()
from hedge.models.gas_dynamics import (
GasDynamicsOperator, PolytropeEOS, GammaLawEOS)
from hedge.mesh import TAG_ALL
# works equally well for GammaLawEOS
op = GasDynamicsOperator(dimensions=2, mu=flow.mu,
prandtl=flow.prandtl, spec_gas_const=flow.spec_gas_const,
equation_of_state=PolytropeEOS(flow.gamma),
bc_inflow=flow, bc_outflow=flow, bc_noslip=flow,
inflow_tag=TAG_ALL, source=None)
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=numpy.float64,
quad_min_degrees={
"gasdyn_vol": 3*order,
"gasdyn_face": 3*order,
},
tune_for=op.op_template(),
debug=["cuda_no_plan"])
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "vortex-%d" % order)
#vis = SiloVisualizer(discr, rcon)
fields = flow.volume_interpolant(0, discr)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
# limiter ------------------------------------------------------------
from hedge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, flow.gamma, 2, op)
from hedge.timestep.runge_kutta import SSP3TimeStepper
#stepper = SSP3TimeStepper(limiter=limiter)
stepper = SSP3TimeStepper(
vector_primitive_factory=discr.get_vector_primitive_factory())
#from hedge.timestep import RK4TimeStepper
#stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "euler-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
final_time = flow.final_time
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
print "run until t=%g" % final_time
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
#true_fields = vortex.volume_interpolant(t, discr)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
#expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
#("p", "0.4*(e- 0.5*(rho_u*u))"),
#],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
#fields = limiter(fields)
assert not numpy.isnan(numpy.sum(fields[0]))
true_fields = flow.volume_interpolant(final_time, discr)
l2_error = discr.norm(fields-true_fields)
l2_error_rho = discr.norm(op.rho(fields)-op.rho(true_fields))
l2_error_e = discr.norm(op.e(fields)-op.e(true_fields))
l2_error_rhou = discr.norm(op.rho_u(fields)-op.rho_u(true_fields))
l2_error_u = discr.norm(op.u(fields)-op.u(true_fields))
eoc_rec.add_data_point(order, l2_error)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
logmgr.set_constant("l2_error_rho", l2_error_rho)
logmgr.set_constant("l2_error_e", l2_error_e)
logmgr.set_constant("l2_error_rhou", l2_error_rhou)
logmgr.set_constant("l2_error_u", l2_error_u)
logmgr.set_constant("refinement", refine)
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
# after order loop
assert eoc_rec.estimate_order_of_convergence()[0,1] > 6
def run_convergence_test_advec(dtype, debug_output=False):
"""Test whether 2/3D advection actually converges"""
from hedge.mesh.generator import make_ball_mesh, make_box_mesh, make_rect_mesh
from hedge.timestep import RK4TimeStepper
from hedge.tools import EOCRecorder
from math import sin, pi, sqrt
from hedge.models.advection import StrongAdvectionOperator
from hedge.data import TimeDependentGivenFunction
from hedge.visualization import SiloVisualizer
from hedge.backends import guess_run_context
rcon = guess_run_context(["mpi"])
# note: x component must remain zero because x-periodicity is used
v = numpy.array([0.0,0.9,0.3])
def f(x):
return sin(x)
def u_analytic(x, el, t):
return f((numpy.dot(-v[:dims],x)/la.norm(v[:dims])+t*la.norm(v[:dims])))
def boundary_tagger(vertices, el, face_nr, points):
face_normal = el.face_normals[face_nr]
if numpy.dot(face_normal, v[:len(face_normal)]) < 0:
return ["inflow"]
else:
return ["outflow"]
for i_mesh, mesh in enumerate([
# 2D semiperiodic
make_rect_mesh(b=(2*pi,3), max_area=0.4,
periodicity=(True, False),
subdivisions=(5,10),
boundary_tagger=boundary_tagger,
),
# 3D x-periodic
make_box_mesh((0,0,0), (2*pi, 2, 2), max_volume=0.4,
periodicity=(True, False, False),
boundary_tagger=boundary_tagger,
),
# non-periodic
make_ball_mesh(r=pi,
boundary_tagger=boundary_tagger, max_volume=0.7),
]):
for flux_type in StrongAdvectionOperator.flux_types:
for random_partition in [True, False]:
eoc_rec = EOCRecorder()
if random_partition:
# Distribute elements randomly across nodes.
# This is bad, efficiency-wise, but it puts stress
# on the parallel implementation, which is desired here.
# Another main point of this is to force the code to split
# a periodic face pair across nodes.
from random import choice
partition = [choice(rcon.ranks) for el in mesh.elements]
else:
partition = None
for order in [1,2,3,4]:
if rcon.is_head_rank:
mesh_data = rcon.distribute_mesh(mesh, partition)
else:
mesh_data = rcon.receive_mesh()
dims = mesh.points.shape[1]
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=dtype)
op = StrongAdvectionOperator(v[:dims],
inflow_u=TimeDependentGivenFunction(u_analytic),
flux_type=flux_type)
if debug_output:
vis = SiloVisualizer(discr, rcon)
u = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, 0))
ic = u.copy()
if debug_output and rcon.is_head_rank:
print "#elements=%d" % len(mesh.elements)
test_name = "test-%s-o%d-m%d-r%s" % (
flux_type, order, i_mesh, random_partition)
rhs = op.bind(discr)
stepper = RK4TimeStepper(dtype=dtype)
from hedge.timestep import times_and_steps
final_time = 1
step_it = times_and_steps(
final_time=final_time,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=u))
for step, t, dt in step_it:
u = stepper(u, t, dt, rhs)
assert u.dtype == dtype
u_true = discr.interpolate_volume_function(
lambda x, el: u_analytic(x, el, final_time))
error = u-u_true
l2_error = discr.norm(error)
if debug_output:
visf = vis.make_file(test_name+"-final")
vis.add_data(visf, [
("u", u),
("u_true", u_true),
("ic", ic)])
visf.close()
eoc_rec.add_data_point(order, l2_error)
if debug_output and rcon.is_head_rank:
print "%s\n%s\n" % (flux_type.upper(), "-" * len(flux_type))
print eoc_rec.pretty_print(abscissa_label="Poly. Order",
error_label="L2 Error")
assert eoc_rec.estimate_order_of_convergence()[0,1] > 3
assert eoc_rec.estimate_order_of_convergence(2)[-1,1] > 7
def main(write_output=True, order=6):
from hedge.data import TimeConstantGivenFunction, \
GivenFunction
from os.path import join
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 3
output_dir = "octahedron"
import os
if not os.access(output_dir, os.F_OK):
os.makedirs(output_dir)
if rcon.is_head_rank:
from hedge.mesh.reader.gmsh import read_gmsh
mesh = read_gmsh("octahedron.msh",
boundary_tagger=lambda x,y,z,w: ["traction"])
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
class Displacement:
shape = (3,)
def __call__(self, x, el):
R = x[0] + x[1] + x[2]
return [-R/30, -R/30, -R/30]
final_time = 3
discr = rcon.make_discretization(mesh_data, order=order,
debug=[])
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, join(output_dir, "test-%d" % order))
if rcon.is_head_rank:
print "order %d" % order
print "#elements=", len(mesh.elements)
from hedge.mesh import TAG_NONE, TAG_ALL
from hedge.models.solid_mechanics import SolidMechanicsOperator
from hedge.models.solid_mechanics.constitutive_laws import NeoHookean
material = NeoHookean(50, 10, 0.3)
op = SolidMechanicsOperator(material,
init_displacement=GivenFunction(Displacement()),
dimensions=discr.dimensions)
fields = op.assemble_vars(discr=discr)
from hedge.timestep import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from time import time
last_tsep = time()
t = 0
# diagnostics setup -------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = join(output_dir, "oct-%d.dat" % order)
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
p_calc = op.bind_stress_calculator(discr)
rhs = op.bind(discr)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, fields=fields))
for step, t, dt in step_it:
u, v = op.split_vars(fields)
P = p_calc(u)
if step % 5 == 0 and write_output:
visf = vis.make_file(join(output_dir, "oct-%d-%04d" % (order, step)))
vis.add_data(visf,
[
("u", discr.convert_volume(u, "numpy")),
("v", discr.convert_volume(v, "numpy")),
("P", discr.convert_volume(P, "numpy"))
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True) :
from math import sin, cos, pi, exp, sqrt
from hedge.data import TimeConstantGivenFunction, \
ConstantGivenFunction
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
def boundary_tagger(fvi, el, fn, all_v):
if el.face_normals[fn][0] > 0:
return ["dirichlet"]
else:
return ["neumann"]
if dim == 2:
if rcon.is_head_rank:
from hedge.mesh.generator import make_disk_mesh
mesh = make_disk_mesh(r=0.5, boundary_tagger=boundary_tagger)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.001)
else:
raise RuntimeError, "bad number of dimensions"
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=3,
debug=["cuda_no_plan"],
default_scalar_type=numpy.float64)
if write_output:
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, rcon, "fld")
def u0(x, el):
if la.norm(x) < 0.2:
return 1
else:
return 0
def coeff(x, el):
if x[0] < 0:
return 0.25
else:
return 1
def dirichlet_bc(t, x):
return 0
def neumann_bc(t, x):
return 2
from hedge.models.diffusion import DiffusionOperator
op = DiffusionOperator(discr.dimensions,
#coeff=coeff,
dirichlet_tag="dirichlet",
dirichlet_bc=TimeConstantGivenFunction(ConstantGivenFunction(0)),
neumann_tag="neumann",
neumann_bc=TimeConstantGivenFunction(ConstantGivenFunction(1))
)
u = discr.interpolate_volume_function(u0)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "heat.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: u
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# timestep loop -----------------------------------------------------------
from hedge.timestep.runge_kutta import LSRK4TimeStepper, ODE45TimeStepper
from hedge.timestep.dumka3 import Dumka3TimeStepper
#stepper = LSRK4TimeStepper()
stepper = Dumka3TimeStepper(3, rtol=1e-6, rcon=rcon,
vector_primitive_factory=discr.get_vector_primitive_factory(),
dtype=discr.default_scalar_type)
#stepper = ODE45TimeStepper(rtol=1e-6, rcon=rcon,
#vector_primitive_factory=discr.get_vector_primitive_factory(),
#dtype=discr.default_scalar_type)
stepper.add_instrumentation(logmgr)
rhs = op.bind(discr)
try:
next_dt = op.estimate_timestep(discr,
stepper=LSRK4TimeStepper(), t=0, fields=u)
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=0.1, logmgr=logmgr,
max_dt_getter=lambda t: next_dt,
taken_dt_getter=lambda: taken_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, [
("u", discr.convert_volume(u, kind="numpy")),
], time=t, step=step)
visf.close()
u, t, taken_dt, next_dt = stepper(u, t, next_dt, rhs)
#u = stepper(u, t, dt, rhs)
assert discr.norm(u) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True, dtype=np.float32):
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
h_fac = 1
mesh = make_rect_mesh(a=(0,0),b=(1,1), max_area=h_fac**2*1e-4,
periodicity=(True,True),
subdivisions=(int(70/h_fac), int(70/h_fac)))
from hedge.models.gas_dynamics.lbm import \
D2Q9LBMMethod, LatticeBoltzmannOperator
op = LatticeBoltzmannOperator(
D2Q9LBMMethod(), lbm_delta_t=0.001, nu=1e-4)
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=3,
default_scalar_type=dtype,
debug=["cuda_no_plan"])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper(dtype=dtype,
#vector_primitive_factory=discr.get_vector_primitive_factory()
)
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
from hedge.data import CompiledExpressionData
def ic_expr(t, x, fields):
from hedge.optemplate import CFunction
from pymbolic.primitives import IfPositive
from pytools.obj_array import make_obj_array
tanh = CFunction("tanh")
sin = CFunction("sin")
rho = 1
u0 = 0.05
w = 0.05
delta = 0.05
from hedge.optemplate.primitives import make_common_subexpression as cse
u = cse(make_obj_array([
IfPositive(x[1]-1/2,
u0*tanh(4*(3/4-x[1])/w),
u0*tanh(4*(x[1]-1/4)/w)),
u0*delta*sin(2*np.pi*(x[0]+1/4))]),
"u")
return make_obj_array([
op.method.f_equilibrium(rho, alpha, u)
for alpha in range(len(op.method))
])
# timestep loop -----------------------------------------------------------
stream_rhs = op.bind_rhs(discr)
collision_update = op.bind(discr, op.collision_update)
get_rho = op.bind(discr, op.rho)
get_rho_u = op.bind(discr, op.rho_u)
f_bar = CompiledExpressionData(ic_expr).volume_interpolant(0, discr)
from hedge.discretization import ExponentialFilterResponseFunction
from hedge.optemplate.operators import FilterOperator
mode_filter = FilterOperator(
ExponentialFilterResponseFunction(min_amplification=0.9, order=4))\
.bind(discr)
final_time = 1000
try:
lbm_dt = op.lbm_delta_t
dg_dt = op.estimate_timestep(discr, stepper=stepper)
print dg_dt
dg_steps_per_lbm_step = int(np.ceil(lbm_dt / dg_dt))
dg_dt = lbm_dt / dg_steps_per_lbm_step
lbm_steps = int(final_time // op.lbm_delta_t)
for step in xrange(lbm_steps):
t = step*lbm_dt
if step % 100 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
rho = get_rho(f_bar)
rho_u = get_rho_u(f_bar)
vis.add_data(visf,
[ ("fbar%d" %i,
discr.convert_volume(f_bar_i, "numpy")) for i, f_bar_i in enumerate(f_bar)]+
[
("rho", discr.convert_volume(rho, "numpy")),
("rho_u", discr.convert_volume(rho_u, "numpy")),
],
time=t,
step=step)
visf.close()
print "step=%d, t=%f" % (step, t)
f_bar = collision_update(f_bar)
for substep in range(dg_steps_per_lbm_step):
f_bar = stepper(f_bar, t + substep*dg_dt, dg_dt, stream_rhs)
#f_bar = mode_filter(f_bar)
finally:
if write_output:
vis.close()
discr.close()
def main():
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import to_obj_array
if rcon.is_head_rank:
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh((-5, -5), (5, 5), max_area=0.01)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [1]:
discr = rcon.make_discretization(mesh_data,
order=order,
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "Sod2D-%d" % order)
#vis = SiloVisualizer(discr, rcon)
sod_field = Sod(gamma=1.4)
fields = sod_field.volume_interpolant(0, discr)
from hedge.models.gas_dynamics import GasDynamicsOperator
from hedge.mesh import TAG_ALL
op = GasDynamicsOperator(dimensions=2,
gamma=sod_field.gamma,
mu=0.0,
prandtl=sod_field.prandtl,
bc_inflow=sod_field,
bc_outflow=sod_field,
bc_noslip=sod_field,
inflow_tag=TAG_ALL,
source=None)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
# limiter setup ------------------------------------------------------------
from hedge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, sod_field.gamma, 2, op)
# integrator setup---------------------------------------------------------
from hedge.timestep import SSPRK3TimeStepper, RK4TimeStepper
stepper = SSPRK3TimeStepper(limiter=limiter)
#stepper = SSPRK3TimeStepper()
#stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
logmgr = LogManager("euler-%d.dat" % order, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# filter setup-------------------------------------------------------------
from hedge.discretization import Filter, ExponentialFilterResponseFunction
mode_filter = Filter(
discr,
ExponentialFilterResponseFunction(min_amplification=0.9, order=4))
# timestep loop -------------------------------------------------------
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=1.0,
logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(
discr, stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 5 == 0:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
#true_fields = vortex.volume_interpolant(t, discr)
#from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(
visf,
[
("rho",
discr.convert_volume(op.rho(fields),
kind="numpy")),
("e",
discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u",
discr.convert_volume(op.rho_u(fields),
kind="numpy")),
("u",
discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", op.rho(true_fields)),
#("true_e", op.e(true_fields)),
#("true_rho_u", op.rho_u(true_fields)),
#("true_u", op.u(true_fields)),
#("rhs_rho", op.rho(rhs_fields)),
#("rhs_e", op.e(rhs_fields)),
#("rhs_rho_u", op.rho_u(rhs_fields)),
],
#expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
#("p", "0.4*(e- 0.5*(rho_u*u))"),
#],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
# fields = limiter(fields)
# fields = mode_filter(fields)
assert not numpy.isnan(numpy.sum(fields[0]))
finally:
vis.close()
logmgr.close()
discr.close()
# not solution, just to check against when making code changes
true_fields = sod_field.volume_interpolant(t, discr)
print discr.norm(fields - true_fields)
def test_with_static_fields():
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
from hedge.discretization.local import TetrahedronDiscretization
from hedge.mesh.generator import \
make_box_mesh, \
make_cylinder_mesh
from hedge.discretization import Discretization
# discretization setup ----------------------------------------------------
radius = 1 * units.M
full_mesh = make_cylinder_mesh(radius=radius,
height=2 * radius,
periodic=True,
radial_subdivisions=30)
from hedge.backends import guess_run_context
pcon = guess_run_context([])
if pcon.is_head_rank:
mesh = pcon.distribute_mesh(full_mesh)
else:
mesh = pcon.receive_mesh()
discr = pcon.make_discretization(mesh, order=1)
# particles setup ---------------------------------------------------------
def get_setup(case):
c = units.VACUUM_LIGHT_SPEED()
from static_field import LarmorScrew, EBParallel
if case == "screw":
return LarmorScrew(units,
mass=units.EL_MASS,
charge=units.EL_CHARGE,
c=c,
vpar=c * 0.8,
vperp=c * 0.1,
bz=1e-3,
nparticles=4)
elif case == "epb":
return EBParallel(units,
mass=units.EL_MASS,
charge=units.EL_CHARGE,
c=c,
ez=1e+5,
bz=1e-3,
radius=0.5 * radius,
nparticles=1)
else:
raise ValueError, "invalid test case"
from pyrticle.pusher import \
MonomialParticlePusher, \
AverageParticlePusher
from static_field import run_setup
for pusher in [MonomialParticlePusher, AverageParticlePusher]:
for case in ["screw", "epb"]:
casename = "%s-%s" % (case, pusher.__class__.__name__.lower())
run_setup(units, casename, get_setup(case), discr, pusher)
def main(write_output=True):
from pytools import add_python_path_relative_to_script
add_python_path_relative_to_script("..")
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.tools import EOCRecorder
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from hedge.mesh.generator import \
make_rect_mesh, \
make_centered_regular_rect_mesh
refine = 4
mesh = make_centered_regular_rect_mesh((0,-5), (10,5), n=(9,9),
post_refine_factor=refine)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
# a second mesh to regrid to
if rcon.is_head_rank:
from hedge.mesh.generator import \
make_rect_mesh, \
make_centered_regular_rect_mesh
refine = 4
mesh2 = make_centered_regular_rect_mesh((0,-5), (10,5), n=(8,8),
post_refine_factor=refine)
mesh_data2 = rcon.distribute_mesh(mesh2)
else:
mesh_data2 = rcon.receive_mesh()
for order in [3,4]:
discr = rcon.make_discretization(mesh_data, order=order,
default_scalar_type=numpy.float64,
quad_min_degrees={
"gasdyn_vol": 3*order,
"gasdyn_face": 3*order,
})
discr2 = rcon.make_discretization(mesh_data2, order=order,
default_scalar_type=numpy.float64,
quad_min_degrees={
"gasdyn_vol": 3*order,
"gasdyn_face": 3*order,
})
from hedge.visualization import SiloVisualizer, VtkVisualizer
vis = VtkVisualizer(discr, rcon, "vortex-%d" % order)
#vis = SiloVisualizer(discr, rcon)
from gas_dynamics_initials import Vortex
vortex = Vortex()
fields = vortex.volume_interpolant(0, discr)
from hedge.models.gas_dynamics import GasDynamicsOperator
from hedge.mesh import TAG_ALL
op = GasDynamicsOperator(dimensions=2, gamma=vortex.gamma, mu=vortex.mu,
prandtl=vortex.prandtl, spec_gas_const=vortex.spec_gas_const,
bc_inflow=vortex, bc_outflow=vortex, bc_noslip=vortex,
inflow_tag=TAG_ALL, source=None)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements for mesh 1 =", len(mesh.elements)
print "#elements for mesh 2 =", len(mesh2.elements)
# limiter ------------------------------------------------------------
from hedge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, vortex.gamma, 2, op)
from hedge.timestep import SSPRK3TimeStepper
#stepper = SSPRK3TimeStepper(limiter=limiter)
stepper = SSPRK3TimeStepper()
#from hedge.timestep import RK4TimeStepper
#stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "euler-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
try:
final_time = 0.2
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
#true_fields = vortex.volume_interpolant(t, discr)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
#expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
#("p", "0.4*(e- 0.5*(rho_u*u))"),
#],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
#fields = limiter(fields)
#regrid to discr2 at some arbitrary time
if step == 21:
#get interpolated fields
fields = discr.get_regrid_values(fields, discr2, dtype=None, use_btree=True, thresh=1e-8)
#get new stepper (old one has reference to discr
stepper = SSPRK3TimeStepper()
#new bind
euler_ex = op.bind(discr2)
#new rhs
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(t+dt, fields)
#add logmanager
#discr2.add_instrumentation(logmgr)
#new step_it
step_it = times_and_steps(
final_time=final_time, logmgr=logmgr,
max_dt_getter=lambda t: op.estimate_timestep(discr2,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
#new visualization
vis.close()
vis = VtkVisualizer(discr2, rcon, "vortexNewGrid-%d" % order)
discr=discr2
assert not numpy.isnan(numpy.sum(fields[0]))
true_fields = vortex.volume_interpolant(final_time, discr)
l2_error = discr.norm(fields-true_fields)
l2_error_rho = discr.norm(op.rho(fields)-op.rho(true_fields))
l2_error_e = discr.norm(op.e(fields)-op.e(true_fields))
l2_error_rhou = discr.norm(op.rho_u(fields)-op.rho_u(true_fields))
l2_error_u = discr.norm(op.u(fields)-op.u(true_fields))
eoc_rec.add_data_point(order, l2_error)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
logmgr.set_constant("l2_error_rho", l2_error_rho)
logmgr.set_constant("l2_error_e", l2_error_e)
logmgr.set_constant("l2_error_rhou", l2_error_rhou)
logmgr.set_constant("l2_error_u", l2_error_u)
logmgr.set_constant("refinement", refine)
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def test_kv_with_no_charge():
from random import seed
seed(0)
from pyrticle.units import SIUnitsWithNaturalConstants
units = SIUnitsWithNaturalConstants()
# discretization setup ----------------------------------------------------
from hedge.mesh import make_cylinder_mesh
from hedge.backends import guess_run_context
rcon = guess_run_context([])
tube_length = 100 * units.MM
mesh = make_cylinder_mesh(radius=25 * units.MM,
height=tube_length,
periodic=True)
discr = rcon.make_discretization(mesh, order=3)
dt = discr.dt_factor(units.VACUUM_LIGHT_SPEED()) / 2
final_time = 1 * units.M / units.VACUUM_LIGHT_SPEED()
nsteps = int(final_time / dt) + 1
dt = final_time / nsteps
# particles setup ---------------------------------------------------------
from pyrticle.cloud import PicMethod
from pyrticle.deposition.shape import ShapeFunctionDepositor
from pyrticle.pusher import MonomialParticlePusher
method = PicMethod(discr, units, ShapeFunctionDepositor(),
MonomialParticlePusher(), 3, 3)
nparticles = 10000
cloud_charge = 1e-9 * units.C
electrons_per_particle = cloud_charge / nparticles / units.EL_CHARGE
el_energy = 5.2e6 * units.EV
gamma = el_energy / units.EL_REST_ENERGY()
beta = (1 - 1 / gamma**2)**0.5
from pyrticle.distribution import KVZIntervalBeam
beam = KVZIntervalBeam(units,
total_charge=0,
p_charge=0,
p_mass=electrons_per_particle * units.EL_MASS,
radii=2 * [2.5 * units.MM],
emittances=2 * [5 * units.MM * units.MRAD],
z_length=5 * units.MM,
z_pos=10 * units.MM,
beta=beta)
state = method.make_state()
method.add_particles(state, beam.generate_particles(), nparticles)
# diagnostics setup -------------------------------------------------------
from pytools.log import LogManager
from pyrticle.log import add_beam_quantities, StateObserver
observer = StateObserver(method, None)
logmgr = LogManager(mode="w")
add_beam_quantities(logmgr, observer, axis=0, beam_axis=2)
from pyrticle.distribution import KVPredictedRadius
logmgr.add_quantity(
KVPredictedRadius(dt,
beam_v=beta * units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_rms_predictor(axis=0),
suffix="x_rms"))
logmgr.add_quantity(
KVPredictedRadius(dt,
beam_v=beta * units.VACUUM_LIGHT_SPEED(),
predictor=beam.get_total_predictor(axis=0),
suffix="x_total"))
# timestep loop -----------------------------------------------------------
vel = method.velocities(state)
from hedge.tools import join_fields
def rhs(t, y):
return join_fields([
vel,
0 * vel,
0, # drecon
])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
t = 0
from pyrticle.cloud import TimesteppablePicState
ts_state = TimesteppablePicState(method, state)
for step in xrange(nsteps):
observer.set_fields_and_state(None, ts_state.state)
logmgr.tick()
ts_state = stepper(ts_state, t, dt, rhs)
method.upkeep(ts_state.state)
t += dt
logmgr.tick()
_, _, err_table = logmgr.get_expr_dataset(
"(rx_rms-rx_rms_theory)/rx_rms_theory")
rel_max_rms_error = max(err for step, err in err_table)
assert rel_max_rms_error < 0.01
def test_mesh_regrid():
"""Test that we are able to interpolate scalars and vectors between two
grids using a spatial binary tree."""
from math import pi, sin, cos
def some_vector(discr):
# x = discr.nodes.T.astype(discr.default_scalar_type)
from hedge.tools import join_fields
u1 = discr.interpolate_volume_function(lambda x, el: sin(pi * x[0]))
u2 = discr.interpolate_volume_function(lambda x, el: sin(pi * x[1]))
u3 = discr.interpolate_volume_function(
lambda x, el: sin(pi * x[0] + pi * x[1]))
u4 = discr.interpolate_volume_function(lambda x, el: cos(pi * x[0]))
return join_fields(u1, u2, u3, u4)
from hedge.backends import guess_run_context
rcon = guess_run_context()
from hedge.mesh.generator import make_centered_regular_rect_mesh
refine = 4
mesh = make_centered_regular_rect_mesh((-1, -1), (2, 2),
n=(7, 7),
post_refine_factor=refine)
discr = rcon.make_discretization(mesh, order=6)
fields_vec = some_vector(discr)
u = discr.interpolate_volume_function(lambda x, el: sin(x[0]))
for el_per_axis in range(2, 4):
for order in range(2, 4):
mesh2 = make_centered_regular_rect_mesh(
(-1, -1), (2, 2),
n=(el_per_axis, el_per_axis),
post_refine_factor=refine)
mesh_data2 = rcon.distribute_mesh(mesh2)
discr2 = rcon.make_discretization(mesh_data2, order=order)
u2 = discr2.interpolate_volume_function(lambda x, el: sin(x[0]))
fields_vec2 = some_vector(discr2)
out = discr.get_regrid_values(u,
discr2,
dtype=None,
use_btree=True,
thresh=1e-7)
out_vec = discr.get_regrid_values(fields_vec,
discr2,
dtype=None,
use_btree=True,
thresh=1e-7)
diff = u2 - out
diff_vec = fields_vec2 - out_vec
L2_vec = discr2.norm(diff_vec)
L2_scalar = discr2.norm(diff)
assert L2_vec < 1e-9
assert L2_scalar < 1e-9
def main(write_output=True):
from hedge.backends import guess_run_context
rcon = guess_run_context(
#["cuda"]
)
gamma = 1.4
# at A=1 we have case of isentropic vortex, source terms
# arise for other values
densityA = 2.0
from hedge.tools import EOCRecorder, to_obj_array
eoc_rec = EOCRecorder()
if rcon.is_head_rank:
from hedge.mesh import \
make_rect_mesh, \
make_centered_regular_rect_mesh
refine = 1
mesh = make_centered_regular_rect_mesh((0,-5), (10,5), n=(9,9),
post_refine_factor=refine)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
for order in [4,5]:
discr = rcon.make_discretization(mesh_data, order=order,
debug=[#"cuda_no_plan",
#"print_op_code"
],
default_scalar_type=numpy.float64)
from hedge.visualization import SiloVisualizer, VtkVisualizer
#vis = VtkVisualizer(discr, rcon, "vortex-%d" % order)
vis = SiloVisualizer(discr, rcon)
vortex = Vortex(beta=5, gamma=gamma,
center=[5,0],
velocity=[1,0], densityA=densityA)
fields = vortex.volume_interpolant(0, discr)
sources=SourceTerms(beta=5, gamma=gamma,
center=[5,0],
velocity=[1,0], densityA=densityA)
from hedge.models.gas_dynamics import (
GasDynamicsOperator, GammaLawEOS)
from hedge.mesh import TAG_ALL
op = GasDynamicsOperator(dimensions=2,
mu=0.0, prandtl=0.72, spec_gas_const=287.1,
equation_of_state=GammaLawEOS(vortex.gamma),
bc_inflow=vortex, bc_outflow=vortex, bc_noslip=vortex,
inflow_tag=TAG_ALL, source=sources)
euler_ex = op.bind(discr)
max_eigval = [0]
def rhs(t, q):
ode_rhs, speed = euler_ex(t, q)
max_eigval[0] = speed
return ode_rhs
rhs(0, fields)
if rcon.is_head_rank:
print "---------------------------------------------"
print "order %d" % order
print "---------------------------------------------"
print "#elements=", len(mesh.elements)
# limiter setup -------------------------------------------------------
from hedge.models.gas_dynamics import SlopeLimiter1NEuler
limiter = SlopeLimiter1NEuler(discr, gamma, 2, op)
# time stepper --------------------------------------------------------
from hedge.timestep import SSPRK3TimeStepper, RK4TimeStepper
#stepper = SSPRK3TimeStepper(limiter=limiter)
#stepper = SSPRK3TimeStepper()
stepper = RK4TimeStepper()
# diagnostics setup ---------------------------------------------------
from pytools.log import LogManager, add_general_quantities, \
add_simulation_quantities, add_run_info
if write_output:
log_file_name = "euler-%d.dat" % order
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
stepper.add_instrumentation(logmgr)
logmgr.add_watches(["step.max", "t_sim.max", "t_step.max"])
# timestep loop -------------------------------------------------------
t = 0
#fields = limiter(fields)
try:
from hedge.timestep import times_and_steps
step_it = times_and_steps(
final_time=.1,
#max_steps=500,
logmgr=logmgr,
max_dt_getter=lambda t: 0.4*op.estimate_timestep(discr,
stepper=stepper, t=t, max_eigenvalue=max_eigval[0]))
for step, t, dt in step_it:
if step % 1 == 0 and write_output:
#if False:
visf = vis.make_file("vortex-%d-%04d" % (order, step))
true_fields = vortex.volume_interpolant(t, discr)
#rhs_fields = rhs(t, fields)
from pyvisfile.silo import DB_VARTYPE_VECTOR
vis.add_data(visf,
[
("rho", discr.convert_volume(op.rho(fields), kind="numpy")),
("e", discr.convert_volume(op.e(fields), kind="numpy")),
("rho_u", discr.convert_volume(op.rho_u(fields), kind="numpy")),
("u", discr.convert_volume(op.u(fields), kind="numpy")),
#("true_rho", discr.convert_volume(op.rho(true_fields), kind="numpy")),
#("true_e", discr.convert_volume(op.e(true_fields), kind="numpy")),
#("true_rho_u", discr.convert_volume(op.rho_u(true_fields), kind="numpy")),
#("true_u", discr.convert_volume(op.u(true_fields), kind="numpy")),
#("rhs_rho", discr.convert_volume(op.rho(rhs_fields), kind="numpy")),
#("rhs_e", discr.convert_volume(op.e(rhs_fields), kind="numpy")),
#("rhs_rho_u", discr.convert_volume(op.rho_u(rhs_fields), kind="numpy")),
],
expressions=[
#("diff_rho", "rho-true_rho"),
#("diff_e", "e-true_e"),
#("diff_rho_u", "rho_u-true_rho_u", DB_VARTYPE_VECTOR),
("p", "0.4*(e- 0.5*(rho_u*u))"),
],
time=t, step=step
)
visf.close()
fields = stepper(fields, t, dt, rhs)
true_fields = vortex.volume_interpolant(t, discr)
l2_error = discr.norm(fields-true_fields)
l2_error_rho = discr.norm(op.rho(fields)-op.rho(true_fields))
l2_error_e = discr.norm(op.e(fields)-op.e(true_fields))
l2_error_rhou = discr.norm(op.rho_u(fields)-op.rho_u(true_fields))
l2_error_u = discr.norm(op.u(fields)-op.u(true_fields))
eoc_rec.add_data_point(order, l2_error_rho)
print
print eoc_rec.pretty_print("P.Deg.", "L2 Error")
logmgr.set_constant("l2_error", l2_error)
logmgr.set_constant("l2_error_rho", l2_error_rho)
logmgr.set_constant("l2_error_e", l2_error_e)
logmgr.set_constant("l2_error_rhou", l2_error_rhou)
logmgr.set_constant("l2_error_u", l2_error_u)
logmgr.set_constant("refinement", refine)
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def test_cuda_volume_quadrature():
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.08)
from hedge.backends import guess_run_context
cpu_rcon = guess_run_context(['jit'])
gpu_rcon = guess_run_context(['cuda'])
order = 4
quad_min_degrees = {"quad": 3 * order}
cpu_discr, gpu_discr = [
rcon.make_discretization(mesh,
order=order,
default_scalar_type=numpy.float64,
debug=[
"cuda_no_plan",
"cuda_no_microblock",
],
quad_min_degrees=quad_min_degrees)
for rcon in [cpu_rcon, gpu_rcon]
]
from math import sin, cos
def f(x, el):
return sin(x[0]) * cos(x[1])
cpu_field, gpu_field = [
discr.interpolate_volume_function(f)
for discr in [cpu_discr, gpu_discr]
]
def make_optemplate():
from hedge.optemplate.operators import QuadratureGridUpsampler
from hedge.optemplate import Field, make_stiffness_t
u = Field("u")
qu = QuadratureGridUpsampler("quad")(u)
return make_stiffness_t(2)[0](Field("intercept")(qu))
saved_vectors = []
def intercept(x):
saved_vectors.append(x)
return x
for discr in [cpu_discr, gpu_discr]:
discr.add_function("intercept", intercept)
opt = make_optemplate()
cpu_bound, gpu_bound = [
discr.compile(make_optemplate())
for discr in [cpu_discr, gpu_discr]
]
cpu_result = cpu_bound(u=cpu_field)
gpu_result = gpu_bound(u=gpu_field)
cpu_ivec, gpu_ivec = saved_vectors
gpu_ivec_on_host = gpu_ivec.get()[gpu_discr._gpu_volume_embedding(
"quad")]
ierr = cpu_ivec - gpu_ivec_on_host
assert la.norm(ierr) < 5e-15
gpu_result_on_host = gpu_discr.convert_volume(gpu_result, kind="numpy")
err = cpu_result - gpu_result_on_host
assert la.norm(err) < 2e-14
cpu_discr.close()
gpu_discr.close()
