def test_1d_mass_mat_trig():
"""Check the integral of some trig functions on an interval using the mass matrix"""
from hedge.mesh.generator import make_uniform_1d_mesh
from hedge.discretization.local import IntervalDiscretization
from math import sqrt, pi, cos, sin
from numpy import dot
mesh = make_uniform_1d_mesh(-4 * pi, 9 * pi, 17, periodic=True)
discr = discr_class(mesh, IntervalDiscretization(8), debug=discr_class.noninteractive_debug_flags())
f = discr.interpolate_volume_function(lambda x, el: cos(x[0]) ** 2)
ones = discr.interpolate_volume_function(lambda x, el: 1)
from hedge.optemplate import MassOperator
mass_op = MassOperator()
num_integral_1 = dot(ones, mass_op.apply(discr, f))
num_integral_2 = dot(f, mass_op.apply(discr, ones))
num_integral_3 = discr.integral(f)
true_integral = 13 * pi / 2
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
err_3 = abs(num_integral_3 - true_integral)
assert err_1 < 1e-10
assert err_2 < 1e-10
assert err_3 < 1e-10
def test_1d_mass_mat_trig():
"""Check the integral of some trig functions on an interval using the mass
matrix
"""
from hedge.mesh.generator import make_uniform_1d_mesh
from hedge.discretization.local import IntervalDiscretization
from math import pi, cos
from numpy import dot
mesh = make_uniform_1d_mesh(-4 * pi, 9 * pi, 17, periodic=True)
discr = discr_class(mesh,
IntervalDiscretization(8),
debug=discr_class.noninteractive_debug_flags())
f = discr.interpolate_volume_function(lambda x, el: cos(x[0])**2)
ones = discr.interpolate_volume_function(lambda x, el: 1)
from hedge.optemplate import MassOperator
mass_op = MassOperator()
num_integral_1 = dot(ones, mass_op.apply(discr, f))
num_integral_2 = dot(f, mass_op.apply(discr, ones))
num_integral_3 = discr.integral(f)
true_integral = 13 * pi / 2
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
err_3 = abs(num_integral_3 - true_integral)
assert err_1 < 1e-10
assert err_2 < 1e-10
assert err_3 < 1e-10
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,
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,
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,
dir_tag=TAG_NONE,
neu_tag=TAG_NONE,
rad_tag=TAG_ALL,
flux_type_arg="upwind"):
from math import sin, cos, pi, exp, sqrt # noqa
from hedge.backends import guess_run_context
rcon = guess_run_context()
dim = 2
if dim == 1:
if rcon.is_head_rank:
from hedge.mesh.generator import make_uniform_1d_mesh
mesh = make_uniform_1d_mesh(-10, 10, 500)
elif dim == 2:
from hedge.mesh.generator import make_rect_mesh
if rcon.is_head_rank:
mesh = make_rect_mesh(a=(-1, -1), b=(1, 1), max_area=0.003)
elif dim == 3:
if rcon.is_head_rank:
from hedge.mesh.generator import make_ball_mesh
mesh = make_ball_mesh(max_volume=0.0005)
else:
raise RuntimeError("bad number of dimensions")
if rcon.is_head_rank:
print "%d elements" % len(mesh.elements)
mesh_data = rcon.distribute_mesh(mesh)
else:
mesh_data = rcon.receive_mesh()
discr = rcon.make_discretization(mesh_data, order=4)
from hedge.timestep.runge_kutta import LSRK4TimeStepper
stepper = LSRK4TimeStepper()
from hedge.visualization import VtkVisualizer
if write_output:
vis = VtkVisualizer(discr, rcon, "fld")
source_center = np.array([0.7, 0.4])
source_width = 1/16
source_omega = 3
import hedge.optemplate as sym
sym_x = sym.nodes(2)
sym_source_center_dist = sym_x - source_center
from hedge.models.wave import VariableVelocityStrongWaveOperator
op = VariableVelocityStrongWaveOperator(
c=sym.If(sym.Comparison(
np.dot(sym_x, sym_x), "<", 0.4**2),
1, 0.5),
dimensions=discr.dimensions,
source=
sym.CFunction("sin")(source_omega*sym.ScalarParameter("t"))
* sym.CFunction("exp")(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2),
dirichlet_tag=dir_tag,
neumann_tag=neu_tag,
radiation_tag=rad_tag,
flux_type=flux_type_arg
)
from hedge.tools import join_fields
fields = join_fields(discr.volume_zeros(),
[discr.volume_zeros() for i in range(discr.dimensions)])
# {{{ diagnostics setup
from pytools.log import LogManager, \
add_general_quantities, \
add_simulation_quantities, \
add_run_info
if write_output:
log_file_name = "wave.dat"
else:
log_file_name = None
logmgr = LogManager(log_file_name, "w", rcon.communicator)
add_run_info(logmgr)
add_general_quantities(logmgr)
add_simulation_quantities(logmgr)
discr.add_instrumentation(logmgr)
from pytools.log import IntervalTimer
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
stepper.add_instrumentation(logmgr)
from hedge.log import LpNorm
u_getter = lambda: fields[0]
logmgr.add_quantity(LpNorm(u_getter, discr, 1, name="l1_u"))
logmgr.add_quantity(LpNorm(u_getter, discr, name="l2_u"))
logmgr.add_watches(["step.max", "t_sim.max", "l2_u", "t_step.max"])
# }}}
# {{{ timestep loop
rhs = op.bind(discr)
try:
from hedge.timestep.stability import \
approximate_rk4_relative_imag_stability_region
max_dt = (
1/discr.compile(op.max_eigenvalue_expr())()
* discr.dt_non_geometric_factor()
* discr.dt_geometric_factor()
* approximate_rk4_relative_imag_stability_region(stepper))
if flux_type_arg == "central":
max_dt *= 0.25
from hedge.timestep import times_and_steps
step_it = times_and_steps(final_time=3, logmgr=logmgr,
max_dt_getter=lambda t: max_dt)
for step, t, dt in step_it:
if step % 10 == 0 and write_output:
visf = vis.make_file("fld-%04d" % step)
vis.add_data(visf,
[
("u", fields[0]),
("v", fields[1:]),
],
time=t,
step=step)
visf.close()
fields = stepper(fields, t, dt, rhs)
assert discr.norm(fields) < 1
finally:
if write_output:
vis.close()
logmgr.close()
discr.close()
def main(write_output=True, flux_type_arg="upwind",
#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, 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, 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, \
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=['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('..')
