def main(write_output=True):
from math import sin, exp, sqrt # noqa
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
from hedge.backends.jit import Discretization
discr = Discretization(mesh, order=4)
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, None, "fld")
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
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE
op = StrongWaveOperator(
-0.1,
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=TAG_NONE,
neumann_tag=TAG_NONE,
radiation_tag=TAG_ALL,
flux_type="upwind")
from hedge.tools import join_fields
fields = join_fields(
discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
nsteps = int(10 / dt)
print "dt=%g nsteps=%d" % (dt, nsteps)
rhs = op.bind(discr)
for step in range(nsteps):
t = step * dt
if step % 10 == 0 and write_output:
print step, t, discr.norm(fields[0])
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)
vis.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 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(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, 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()
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, 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 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()
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
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, \
dir_tag=TAG_NONE, \
neu_tag=TAG_NONE,\
rad_tag=TAG_ALL,
flux_type_arg="upwind"):
from math import sin, cos, pi, exp, sqrt
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 import RK4TimeStepper
stepper = RK4TimeStepper()
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
def source_u(x, el):
x = x - numpy.array([0.7, 0.4])
return exp(-numpy.dot(x, x)*256)
def c_speed(x, el):
if la.norm(x) < 0.4:
return 1
else:
return 0.5
from hedge.models.wave import VariableVelocityStrongWaveOperator
from hedge.data import \
TimeIntervalGivenFunction, \
make_tdep_given
from hedge.mesh import TAG_ALL, TAG_NONE
op = VariableVelocityStrongWaveOperator(
make_tdep_given(c_speed),
discr.dimensions,
source=TimeIntervalGivenFunction(
make_tdep_given(source_u),
0, 0.1),
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 Integral, 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:
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
if flux_type_arg == "central":
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: 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:]),
("c", op.c.volume_interpolant(0, discr)),
],
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,
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(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 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 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,
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()
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(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(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):
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()
# 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 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):
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=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):
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):
from math import sin, exp, sqrt
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-0.5,-0.5),b=(0.5,0.5),max_area=0.008)
from hedge.backends.jit import Discretization
discr = Discretization(mesh, order=4)
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, None, "fld")
def source_u(x, el):
x = x - numpy.array([0.1,0.22])
return exp(-numpy.dot(x, x)*128)
from hedge.data import \
make_tdep_given, \
TimeHarmonicGivenFunction, \
TimeIntervalGivenFunction
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE
op = StrongWaveOperator(-1, discr.dimensions,
source_f=TimeIntervalGivenFunction(
TimeHarmonicGivenFunction(
make_tdep_given(source_u), omega=10),
0, 1),
dirichlet_tag=TAG_NONE,
neumann_tag=TAG_NONE,
radiation_tag=TAG_ALL,
flux_type="upwind")
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
from hedge.timestep import RK4TimeStepper
stepper = RK4TimeStepper()
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
nsteps = int(1/dt)
print "dt=%g nsteps=%d" % (dt, nsteps)
rhs = op.bind(discr)
for step in range(nsteps):
t = step*dt
if step % 50 == 0 and write_output:
print step, t, discr.norm(fields[0])
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)
vis.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(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 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, 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):
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(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, 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(write_output=True):
from math import sin, exp, sqrt # noqa
from hedge.mesh.generator import make_rect_mesh
mesh = make_rect_mesh(a=(-0.5, -0.5), b=(0.5, 0.5), max_area=0.008)
from hedge.backends.jit import Discretization
discr = Discretization(mesh, order=4)
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, None, "fld")
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
from hedge.models.wave import StrongWaveOperator
from hedge.mesh import TAG_ALL, TAG_NONE
op = StrongWaveOperator(-0.1, 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=TAG_NONE,
neumann_tag=TAG_NONE,
radiation_tag=TAG_ALL,
flux_type="upwind")
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
dt = op.estimate_timestep(discr, stepper=stepper, fields=fields)
nsteps = int(10/dt)
print "dt=%g nsteps=%d" % (dt, nsteps)
rhs = op.bind(discr)
for step in range(nsteps):
t = step*dt
if step % 10 == 0 and write_output:
print step, t, discr.norm(fields[0])
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)
vis.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():
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 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=['vtu', 'receivers'],
allow_features='',
dim=2,
order=4,
stfree_tag=TAG_NONE,
fix_tag=TAG_ALL,
op_tag=TAG_NONE,
flux_type="lf",
max_steps=None,
output_dir='output',
pml=None,
sources=None,
source_param={},
final_time=12,
quiet_output=True,
nonlinearity_type=None,
mesh_file='',
periodicity=None,
material_files=None,
vtu_every=20):
"""
Parameters:
@param write_output: output data, among 'vtu', 'receivers' and 'txt'
@param allow_features: 'mpi' or 'cuda'
@param dim: 1, 2 or 3
@param order: the order of the method
@param stfree_tag: which elements to mark as stress-free boundaries
@param fix_tag: which elements to mark as fixed boundaries
@param op_tag: which elements to mark as open boundaries
@param flux_type: 'lf' (Lax-Freidrich flux) or 'central'
@param max_steps: None (no limit) or maximum number of steps to compute
@param output_dir: directory where to write the output
@param pml: None or NPML widths in this order: [x_l, y_l, z_l, x_r, y_r, z_r]
@param sources: an array containing the coordinates of the source or None
@param source_param: a dict containing the parameters for the source functions
@param final_time: number of seconds of simulations to compute
@param quiet_output: if True, only the main thread will print information
@param nonlinearity_type: None (linear) or 'classical' (non-linear)
@param mesh_file: the file to use as a mesh, or '' in 1D
@param periodicity: the names of the boundaries to stick together, or None
@param material_files: array, the material files (.dat) to use
@param vtu_every: n, to write a vtu file every n steps
"""
rcon = guess_run_context(allow_features)
rcon_init = guess_run_context(allow_features)
debug = ['dump_optemplate_stages']
dtype = numpy.float64
if 'cuda' in allow_features:
dtype = numpy.float32
debug.append('cuda_no_plan')
if rcon.is_head_rank and output_dir and not access(output_dir, F_OK):
makedirs(output_dir)
if quiet_output:
print_output = rcon.is_head_rank
else:
print_output = True
if print_output:
print "Using features:", ', '.join(allow_features).upper()
nbranks = len(rcon.ranks)
print "Using", nbranks, "rank" + ('s' if nbranks > 1 else '')
print "Using", dim, "dimension" + ('s' if dim > 1 else '')
print "Rank", rcon.rank, "will print its output."
else:
print "Rank", rcon.rank, "will be silent."
class Receiver():
pass
assert dim in [1, 2, 3], 'Bad number of dimensions'
# Define mesh ---
mesh = None
if mesh_file != '':
mesh = read_gmsh(mesh_file,
force_dimension=dim,
periodicity=periodicity,
allow_internal_boundaries=False,
tag_mapper=lambda tag: tag)
elif dim == 1:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
else:
raise Exception('Error: No mesh file specified!')
if rcon.is_head_rank:
print "Using %d elements and order %d" % (len(mesh.elements), order)
mesh_data = rcon.distribute_mesh(mesh)
mesh_init = rcon_init.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
mesh_init = rcon_init.receive_mesh()
if mesh_file:
from libraries.gmsh_reader import GmshReader
gmsh = GmshReader(mesh_file, dim, print_output)
# End of mesh definition ---
# Define sources ---
source = None
if sources is not None:
#FIXME: "Multiple source points are currently unsupported"
source = sources
if print_output:
print "Using specified source", source
else:
if print_output:
print "No source specified",
if mesh_file:
if print_output:
print "trying to find one in", mesh_file
sources = gmsh.pointSources
if sources != []:
source = sources[0]
if print_output:
print "Using source", source, "from", mesh_file
else:
if print_output:
print "Error: no source!"
else:
if print_output:
print "and no mesh file!"
raise Exception('Error: Could not find any source!')
def source_v_x(pos, el):
pos = pos - source
#return exp(-numpy.dot(pos, pos) / source_param['sigma'] ** 2)
return exp(- pos[0]**2 / source_param['sigma'] ** 2)
def source_v_y(pos, el):
pos = pos - source
return 0
def source_v_z(pos, el):
pos = pos - source
return 0
source_type = None
if source_param['type'] == 'Sinus':
from libraries.functions import SinusGivenFunction
source_type = 'SinusGivenFunction'
elif source_param['type'] == 'SineBurst':
from libraries.functions import SineBurstGivenFunction
source_type = 'SineBurstGivenFunction'
elif source_param['type'] == 'Modulated_sinus':
from libraries.functions import ModulatedSinusGivenFunction
source_type = 'ModulatedSinusGivenFunction'
elif source_param['type'] == 'Ricker':
from libraries.functions import TimeRickerWaveletGivenFunction
source_type = 'TimeRickerWaveletGivenFunction'
assert source_type is not None, "Failed to define source function!"
source_function = locals()[source_type]
print "Using source type:", source_type
from hedge.data import make_tdep_given, TimeIntervalGivenFunction
def source_i(source_v_i):
return TimeIntervalGivenFunction(
source_function(make_tdep_given(source_v_i),
source_param['fc'], source_param['td']),
source_param['begin'], source_param['end'])
sources = {'source_x': source_i(source_v_x),
'source_y': source_i(source_v_y),
'source_z': source_i(source_v_z)}
# End of sources definition ---
# Define materials and link them with elements ---
materials = []
constants = ['Density', 'LinearElasticConstants']
if nonlinearity_type == 'cubic':
constants.append('ElasticConstant_lambda')
constants.append('ElasticConstant_mu')
constants.append('QuadraticElasticConstant_f')
constants.append('CubicElasticConstant_h')
elif nonlinearity_type is not None:
constants.append('NonlinearElasticConstants')
for material_file in material_files:
material = Material(material_file, constants, dtype, print_output)
if nonlinearity_type == 'cubic':
assert material.lambda_ is not None, "Error: Missing elastic constant lambda in " + file
assert material.mu is not None, "Error: Missing elastic constant mu in " + file
assert material.f is not None, "Error: Missing quadratic constant f in " + file
assert material.h is not None, "Error: Missing cubic constant h in " + file
elif nonlinearity_type is not None:
# In the nonlinear mode, materials MUST have a nonlinear constants
assert material.Cnl is not None, "Error: Missing nonlinear constants in " + file
materials.append(material)
assert len(materials) > 0, "Error: You must define at least 1 material."
# Work out which elements belong to each material
material_elements = []
used_materials = []
speeds = []
for num, name in [(0, 'mat1'), (1, 'mat2'), (2, 'mat3')]:
if len(materials) > num:
if name in mesh_init.tag_to_elements.keys():
elements_list = [el.id for el in mesh_init.tag_to_elements[name]]
material_elements.append(elements_list)
else:
num = 0
speed = (materials[num].C[0, 0] / materials[num].rho) ** 0.5
speeds.append(speed.astype(dtype))
used_materials.append(materials[num])
if print_output:
print "Using", materials[num].filename, "as", name
speed = max(speeds)
if print_output:
print "Using max speed:", speed, "m/s"
def mat_val(x, el):
# Will be used in Evaluate(mat, val)
for i in range(len(material_elements)):
if el.id in material_elements[i]:
return i
return 0
# End of materials definition ---
# Define the elastodynamics operator and the discretization ---
kwargs = {
'dimensions': dim,
'speed': speed,
'material': make_tdep_given(mat_val),
'sources': sources,
'boundaryconditions_tag': \
{'stressfree': stfree_tag,
'fixed': fix_tag,
'open': op_tag},
'materials': used_materials,
'flux_type': flux_type
}
operator = None
if nonlinearity_type == 'cubic':
kwargs['nonlinearity_type'] = nonlinearity_type
if pml:
from elastodynamic import CubicNPMLElastoDynamicsOperator
operator = 'CubicNPMLElastoDynamicsOperator'
else:
raise NotImplementedError
elif nonlinearity_type is not None:
kwargs['nonlinearity_type'] = nonlinearity_type
if pml:
from elastodynamic import QuadraticNPMLElastoDynamicsOperator
operator = 'QuadraticNPMLElastoDynamicsOperator'
else:
from elastodynamic import QuadraticElastoDynamicsOperator
operator = 'QuadraticElastoDynamicsOperator'
else:
if pml:
from elastodynamic import NPMLElastoDynamicsOperator
operator = "NPMLElastoDynamicsOperator"
else:
from elastodynamic import ElastoDynamicsOperator
operator = "ElastoDynamicsOperator"
assert operator is not None, "Failed to define operator!"
op = locals()[operator](**kwargs)
if print_output:
print "Using", operator
discr = rcon.make_discretization(mesh_data, order=order, debug=debug, tune_for=op.op_template())
# End of elastodynamics operator and discretization definition ---
# Define receivers ---
receivers = []
point_receivers = []
if write_output and print_output:
print "Using output dir:", output_dir
if "receivers" in write_output:
i = 0
if mesh_file:
receivers = gmsh.pointReceivers
if receivers != []:
for receiver in receivers:
try:
point_receiver = Receiver()
point_receiver.evaluator = discr.get_point_evaluator(numpy.array(receiver))
point_receiver.done_dt = False
point_receiver.id = i
point_receiver.coordinates = receiver
point_receiver.filename = "receiver_%s.txt" % repr(point_receiver.coordinates)
except:
if not quiet_output:
print "Receiver ignored (point not found):", receiver
else:
point_receivers.append(point_receiver)
i += 1
print "Using", point_receiver.filename, "for receiver", receiver
# End of receivers definition ---
# Define visualization ---
def write_datafile(filename, variables):
if rcon is not None and len(rcon.ranks) > 1:
filename += "-%04d" % rcon.rank
visfile = open(filename + ".txt", "wt")
visfile.write("x\ty\t")
for name, field in variables:
if name == "m":
visfile.write("m\t")
else:
i = 0
for subvect in field:
i += 1
assert len(subvect) == len(discr.nodes), "Wrong length!"
visfile.write(name + "_" + format(i) + "\t")
visfile.write("\n")
for i in range(len(discr.nodes)):
for coord in discr.nodes[i]:
visfile.write(format(coord) + "\t")
for name, field in variables:
if name == "m":
visfile.write(format(field[i]) + "\t")
else:
for subvect in field:
visfile.write(format(subvect[i]) + "\t")
visfile.write("\n")
visfile.close()
if 'vtu' in write_output:
from hedge.visualization import VtkVisualizer
vis = VtkVisualizer(discr, rcon, 'fld')
if output_dir:
chdir(output_dir)
if 'receivers' in write_output:
for point_receiver in point_receivers:
point_receiver.pointfile = open(point_receiver.filename, "wt")
#sumfile = open("receiver_%s_sum.txt" % rcon.rank, "wt")
# End of visualization definition ---
# Bind the operator to the discretization ---
if pml:
coefficients = op.coefficients_from_width(discr, mesh, widths=pml,
material=materials[0],
alpha_magnitude=2 * pi * source_param['fc'] / 10)
rhs = op.bind(discr, coefficients)
else:
rhs = op.bind(discr)
# End of operator binding ---
# Define the timestep loop ---
t = 0.0
max_txt = ''
try:
len_fields = op.len_q
if pml:
len_fields += op.len_f2
fields = make_obj_array([discr.volume_zeros(dtype=dtype) for _ in range(len_fields)])
vector_primitive_factory = None if 'cuda' in allow_features else discr.get_vector_primitive_factory()
from hedge.timestep import times_and_steps, LSRK4TimeStepper
stepper = LSRK4TimeStepper(vector_primitive_factory=vector_primitive_factory, dtype=dtype)
max_dt_getter = lambda t: op.estimate_timestep(discr, stepper=stepper, t=t, fields=fields)
step_it = times_and_steps(final_time=final_time, logmgr=None, max_dt_getter=max_dt_getter)
for step, t, dt in step_it:
if max_steps > 0:
max_txt = ' on %d' % max_steps
if step > max_steps:
break
if step % vtu_every == 0:
variables = [("m", discr.convert_volume(op.m(fields), "numpy")),
("v", discr.convert_volume(op.v(fields), "numpy")),
("F", discr.convert_volume(op.F(fields), "numpy"))]
if print_output:
print time.strftime('[%H:%M:%S] ', time.localtime()) + \
'Step: ' + format(step) + max_txt + '; time: ' + format(t)
if 'vtu' in write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf, variables, time=t, step=step)
visf.close()
if 'txt' in write_output:
write_datafile("fld-%04d" % step, variables)
if 'receivers' in write_output and point_receivers != []:
variables = discr.convert_volume(fields, "numpy")
#sum_val = numpy.zeros(len(fields))
#sumfile.write("\n%s " % format(t))
for point_receiver in point_receivers:
val = point_receiver.evaluator(variables)
if not point_receiver.done_dt:
point_receiver.pointfile.write("# dt: %g s\n" % dt)
point_receiver.pointfile.write("# m: 1 field\n")
point_receiver.pointfile.write("# v: %d fields\n" % dim)
point_receiver.pointfile.write("# F: %d fields\n" % op.len_f)
point_receiver.pointfile.write("# Coordinates: %s\n# t m " % repr(point_receiver.coordinates))
for i in range(dim):
point_receiver.pointfile.write('v%s ' % i)
for i in range(op.len_f):
point_receiver.pointfile.write("F%s " % i)
point_receiver.done_dt = True
point_receiver.pointfile.write("\n%s " % format(t))
for i in range(1 + dim + op.len_f):
#sum_val[i] += val[i]
point_receiver.pointfile.write("%s " % format(val[i]))
#for i in range(len(val)):
#sumfile.write("%s " % format(sum_val[i]))
fields = stepper(fields, t, dt, rhs)
finally:
if 'vtu' in write_output:
vis.close()
if 'receivers' in write_output:
for point_receiver in point_receivers:
point_receiver.pointfile.close()
#sumfile.close()
discr.close()
if output_dir:
chdir('..')
