def get_rectangular_cavity_mode(E_0, mode_indices): # noqa: N803
"""A rectangular TM cavity mode for a rectangle / cube
with one corner at the origin and the other at (1,1[,1])."""
dims = len(mode_indices)
if dims != 2 and dims != 3:
raise ValueError("Improper mode_indices dimensions")
import numpy
factors = [n * numpy.pi for n in mode_indices]
kx, ky = factors[0:2]
if dims == 3:
kz = factors[2]
omega = numpy.sqrt(sum(f**2 for f in factors))
nodes = sym.nodes(dims)
x = nodes[0]
y = nodes[1]
if dims == 3:
z = nodes[2]
sx = sym.sin(kx * x)
cx = sym.cos(kx * x)
sy = sym.sin(ky * y)
cy = sym.cos(ky * y)
if dims == 3:
sz = sym.sin(kz * z)
cz = sym.cos(kz * z)
if dims == 2:
tfac = sym.ScalarVariable("t") * omega
result = flat_obj_array(
0,
0,
sym.sin(kx * x) * sym.sin(ky * y) * sym.cos(tfac), # ez
-ky * sym.sin(kx * x) * sym.cos(ky * y) * sym.sin(tfac) /
omega, # hx
kx * sym.cos(kx * x) * sym.sin(ky * y) * sym.sin(tfac) /
omega, # hy
0,
)
else:
tdep = sym.exp(-1j * omega * sym.ScalarVariable("t"))
gamma_squared = ky**2 + kx**2
result = flat_obj_array(
-kx * kz * E_0 * cx * sy * sz * tdep / gamma_squared, # ex
-ky * kz * E_0 * sx * cy * sz * tdep / gamma_squared, # ey
E_0 * sx * sy * cz * tdep, # ez
-1j * omega * ky * E_0 * sx * cy * cz * tdep / gamma_squared, # hx
1j * omega * kx * E_0 * cx * sy * cz * tdep / gamma_squared,
0,
)
return result
def simple_mpi_communication_entrypoint():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
from meshmode.mesh import BTAG_ALL
from mpi4py import MPI
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
mesh_dist = MPIMeshDistributor(comm)
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-1, ) * 2,
b=(1, ) * 2,
nelements_per_axis=(2, ) * 2)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
else:
local_mesh = mesh_dist.receive_mesh_part()
vol_discr = DiscretizationCollection(actx,
local_mesh,
order=5,
mpi_communicator=comm)
sym_x = sym.nodes(local_mesh.dim)
myfunc_symb = sym.sin(np.dot(sym_x, [2, 3]))
myfunc = bind(vol_discr, myfunc_symb)(actx)
sym_all_faces_func = sym.cse(
sym.project("vol", "all_faces")(sym.var("myfunc")))
sym_int_faces_func = sym.cse(
sym.project("vol", "int_faces")(sym.var("myfunc")))
sym_bdry_faces_func = sym.cse(
sym.project(BTAG_ALL,
"all_faces")(sym.project("vol",
BTAG_ALL)(sym.var("myfunc"))))
bound_face_swap = bind(
vol_discr,
sym.project("int_faces", "all_faces")(
sym.OppositeInteriorFaceSwap("int_faces")(sym_int_faces_func)) -
(sym_all_faces_func - sym_bdry_faces_func))
hopefully_zero = bound_face_swap(myfunc=myfunc)
error = actx.np.linalg.norm(hopefully_zero, ord=np.inf)
print(__file__)
with np.printoptions(threshold=100000000, suppress=True):
logger.debug(hopefully_zero)
logger.info("error: %.5e", error)
assert error < 1e-14
def simple_mpi_communication_entrypoint():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
from mpi4py import MPI
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
mesh_dist = MPIMeshDistributor(comm)
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-1, ) * 2,
b=(1, ) * 2,
n=(3, ) * 2)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
else:
local_mesh = mesh_dist.receive_mesh_part()
vol_discr = DGDiscretizationWithBoundaries(cl_ctx,
local_mesh,
order=5,
mpi_communicator=comm)
sym_x = sym.nodes(local_mesh.dim)
myfunc_symb = sym.sin(np.dot(sym_x, [2, 3]))
myfunc = bind(vol_discr, myfunc_symb)(queue)
sym_all_faces_func = sym.cse(
sym.interp("vol", "all_faces")(sym.var("myfunc")))
sym_int_faces_func = sym.cse(
sym.interp("vol", "int_faces")(sym.var("myfunc")))
sym_bdry_faces_func = sym.cse(
sym.interp(sym.BTAG_ALL,
"all_faces")(sym.interp("vol",
sym.BTAG_ALL)(sym.var("myfunc"))))
bound_face_swap = bind(
vol_discr,
sym.interp("int_faces", "all_faces")(
sym.OppositeInteriorFaceSwap("int_faces")(sym_int_faces_func)) -
(sym_all_faces_func - sym_bdry_faces_func))
# print(bound_face_swap)
# 1/0
hopefully_zero = bound_face_swap(queue, myfunc=myfunc)
import numpy.linalg as la
error = la.norm(hopefully_zero.get())
np.set_printoptions(threshold=100000000, suppress=True)
print(hopefully_zero)
print(error)
assert error < 1e-14
def get_strong_wave_op_with_discr(cl_ctx, dims=2, order=4):
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(16, ) * dims)
logger.debug("%d elements", mesh.nelements)
discr = DGDiscretizationWithBoundaries(cl_ctx, mesh, order=order)
source_center = np.array([0.1, 0.22, 0.33])[:dims]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(
-0.1,
dims,
source_f=(
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
op.check_bc_coverage(mesh)
return (op.sym_operator(), discr)
def _get_source_term(dims):
source_center = np.array([0.1, 0.22, 0.33])[:dims]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(dims)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
return (sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2))
def get_strong_wave_op_with_discr_direct(cl_ctx, dims=2, order=4):
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(16, ) * dims)
logger.debug("%d elements", mesh.nelements)
discr = DGDiscretizationWithBoundaries(cl_ctx, mesh, order=order)
source_center = np.array([0.1, 0.22, 0.33])[:dims]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from meshmode.mesh import BTAG_ALL
c = -0.1
sign = -1
w = sym.make_sym_array("w", dims + 1)
u = w[0]
v = w[1:]
source_f = (
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2))
rad_normal = sym.normal(BTAG_ALL, dims)
rad_u = sym.cse(sym.interp("vol", BTAG_ALL)(u))
rad_v = sym.cse(sym.interp("vol", BTAG_ALL)(v))
rad_bc = sym.cse(
sym.join_fields(
0.5 * (rad_u - sign * np.dot(rad_normal, rad_v)),
0.5 * rad_normal * (np.dot(rad_normal, rad_v) - sign * rad_u)),
"rad_bc")
sym_operator = (
-sym.join_fields(-c * np.dot(sym.nabla(dims), v) - source_f, -c *
(sym.nabla(dims) * u)) + sym.InverseMassOperator()(
sym.FaceMassOperator()
(dg_flux(c, sym.int_tpair(w)) +
dg_flux(c, sym.bv_tpair(BTAG_ALL, w, rad_bc)))))
return (sym_operator, discr)
def test_tri_diff_mat(ctx_factory, dim, order=4):
"""Check differentiation matrix along the coordinate axes on a disk
Uses sines as the function to differentiate.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from meshmode.mesh.generation import generate_regular_rect_mesh
from pytools.convergence import EOCRecorder
axis_eoc_recs = [EOCRecorder() for axis in range(dim)]
for n in [10, 20]:
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(n, ) * dim,
order=4)
discr = DGDiscretizationWithBoundaries(actx, mesh, order=4)
nabla = sym.nabla(dim)
for axis in range(dim):
x = sym.nodes(dim)
f = bind(discr, sym.sin(3 * x[axis]))(actx)
df = bind(discr, 3 * sym.cos(3 * x[axis]))(actx)
sym_op = nabla[axis](sym.var("f"))
bound_op = bind(discr, sym_op)
df_num = bound_op(f=f)
linf_error = flat_norm(df_num - df, np.Inf)
axis_eoc_recs[axis].add_data_point(1 / n, linf_error)
for axis, eoc_rec in enumerate(axis_eoc_recs):
logger.info("axis %d\n%s", axis, eoc_rec)
assert eoc_rec.order_estimate() >= order
def test_tri_diff_mat(actx_factory, dim, order=4):
"""Check differentiation matrix along the coordinate axes on a disk
Uses sines as the function to differentiate.
"""
actx = actx_factory()
from pytools.convergence import EOCRecorder
axis_eoc_recs = [EOCRecorder() for axis in range(dim)]
for n in [4, 8, 16]:
mesh = mgen.generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(n, ) * dim,
order=4)
discr = DiscretizationCollection(actx, mesh, order=4)
nabla = sym.nabla(dim)
for axis in range(dim):
x = sym.nodes(dim)
f = bind(discr, sym.sin(3 * x[axis]))(actx)
df = bind(discr, 3 * sym.cos(3 * x[axis]))(actx)
sym_op = nabla[axis](sym.var("f"))
bound_op = bind(discr, sym_op)
df_num = bound_op(f=f)
linf_error = actx.np.linalg.norm(df_num - df, ord=np.inf)
axis_eoc_recs[axis].add_data_point(1 / n, linf_error)
for axis, eoc_rec in enumerate(axis_eoc_recs):
logger.info("axis %d\n%s", axis, eoc_rec)
assert eoc_rec.order_estimate() > order - 0.25
def f(x):
return sym.sin(3 * x)
def f(x):
return sym.sin(10 * x)
def f(x):
return flat_obj_array(
sym.sin(3 * x[0]) + sym.cos(3 * x[1]),
sym.sin(2 * x[0]) + sym.cos(x[1]))
def main(write_output=True, order=4):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
dims = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(16, ) * dims)
if mesh.dim == 2:
dt = 0.04
elif mesh.dim == 3:
dt = 0.02
print("%d elements" % mesh.nelements)
discr = DGDiscretizationWithBoundaries(cl_ctx, mesh, order=order)
source_center = np.array([0.1, 0.22, 0.33])[:mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(
-0.1,
discr.dim,
source_f=(
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
queue = cl.CommandQueue(discr.cl_context)
from pytools.obj_array import join_fields
fields = join_fields(discr.zeros(queue),
[discr.zeros(queue) for i in range(discr.dim)])
# FIXME
#dt = op.estimate_rk4_timestep(discr, fields=fields)
op.check_bc_coverage(mesh)
# print(sym.pretty(op.sym_operator()))
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(queue, t=t, w=w)
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 10
nsteps = int(final_t / dt)
print("dt=%g nsteps=%d" % (dt, nsteps))
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=order)
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(queue, u=event.state_component[0]),
time() - t_last_step)
if step % 10 == 0:
vis.write_vtk_file("fld-wave-min-%04d.vtu" % step, [
("u", event.state_component[0]),
("v", event.state_component[1:]),
])
t_last_step = time()
def mpi_communication_entrypoint():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from mpi4py import MPI
comm = MPI.COMM_WORLD
i_local_rank = comm.Get_rank()
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
dt = 0.04
order = 4
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(16, ) * dim)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
else:
local_mesh = mesh_dist.receive_mesh_part()
vol_discr = DGDiscretizationWithBoundaries(cl_ctx,
local_mesh,
order=order,
mpi_communicator=comm)
source_center = np.array([0.1, 0.22, 0.33])[:local_mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(local_mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(
-0.1,
vol_discr.dim,
source_f=(
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
from pytools.obj_array import join_fields
fields = join_fields(
vol_discr.zeros(queue),
[vol_discr.zeros(queue) for i in range(vol_discr.dim)])
# FIXME
# dt = op.estimate_rk4_timestep(vol_discr, fields=fields)
# FIXME: Should meshmode consider BTAG_PARTITION to be a boundary?
# Fails because: "found faces without boundary conditions"
# op.check_bc_coverage(local_mesh)
from pytools.log import LogManager, \
add_general_quantities, \
add_run_info, \
IntervalTimer, EventCounter
log_filename = None
# NOTE: LogManager hangs when using a file on a shared directory.
# log_filename = 'grudge_log.dat'
logmgr = LogManager(log_filename, "w", comm)
add_run_info(logmgr)
add_general_quantities(logmgr)
log_quantities =\
{"rank_data_swap_timer": IntervalTimer("rank_data_swap_timer",
"Time spent evaluating RankDataSwapAssign"),
"rank_data_swap_counter": EventCounter("rank_data_swap_counter",
"Number of RankDataSwapAssign instructions evaluated"),
"exec_timer": IntervalTimer("exec_timer",
"Total time spent executing instructions"),
"insn_eval_timer": IntervalTimer("insn_eval_timer",
"Time spend evaluating instructions"),
"future_eval_timer": IntervalTimer("future_eval_timer",
"Time spent evaluating futures"),
"busy_wait_timer": IntervalTimer("busy_wait_timer",
"Time wasted doing busy wait")}
for quantity in log_quantities.values():
logmgr.add_quantity(quantity)
# print(sym.pretty(op.sym_operator()))
bound_op = bind(vol_discr, op.sym_operator())
# print(bound_op)
# 1/0
def rhs(t, w):
val, rhs.profile_data = bound_op(queue,
profile_data=rhs.profile_data,
log_quantities=log_quantities,
t=t,
w=w)
return val
rhs.profile_data = {}
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 4
nsteps = int(final_t / dt)
print("rank=%d dt=%g nsteps=%d" % (i_local_rank, dt, nsteps))
# from grudge.shortcuts import make_visualizer
# vis = make_visualizer(vol_discr, vis_order=order)
step = 0
norm = bind(vol_discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
logmgr.tick_before()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(queue, u=event.state_component[0]),
time() - t_last_step)
# if step % 10 == 0:
# vis.write_vtk_file("rank%d-fld-%04d.vtu" % (i_local_rank, step),
# [("u", event.state_component[0]),
# ("v", event.state_component[1:])])
t_last_step = time()
logmgr.tick_after()
logmgr.tick_before()
logmgr.tick_after()
def print_profile_data(data):
print("""execute() for rank %d:
\tInstruction Evaluation: %f%%
\tFuture Evaluation: %f%%
\tBusy Wait: %f%%
\tTotal: %f seconds""" %
(i_local_rank, data['insn_eval_time'] / data['total_time'] * 100,
data['future_eval_time'] / data['total_time'] * 100,
data['busy_wait_time'] / data['total_time'] * 100,
data['total_time']))
print_profile_data(rhs.profile_data)
logmgr.close()
logger.debug("Rank %d exiting", i_local_rank)
def simple_wave_entrypoint(dim=2, num_elems=256, order=4, num_steps=30,
log_filename="grudge.dat"):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from mpi4py import MPI
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
n = int(num_elems ** (1./dim))
from meshmode.distributed import MPIMeshDistributor
mesh_dist = MPIMeshDistributor(comm)
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5,)*dim,
b=(0.5,)*dim,
n=(n,)*dim)
from pymetis import part_graph
_, p = part_graph(num_parts,
xadj=mesh.nodal_adjacency.neighbors_starts.tolist(),
adjncy=mesh.nodal_adjacency.neighbors.tolist())
part_per_element = np.array(p)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element, num_parts)
else:
local_mesh = mesh_dist.receive_mesh_part()
vol_discr = DGDiscretizationWithBoundaries(cl_ctx, local_mesh, order=order,
mpi_communicator=comm)
source_center = np.array([0.1, 0.22, 0.33])[:local_mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(local_mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(-0.1, vol_discr.dim,
source_f=(
sym.sin(source_omega*sym_t)
* sym.exp(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
from pytools.obj_array import join_fields
fields = join_fields(vol_discr.zeros(queue),
[vol_discr.zeros(queue) for i in range(vol_discr.dim)])
from logpyle import LogManager, \
add_general_quantities, \
add_run_info, \
IntervalTimer, EventCounter
# NOTE: LogManager hangs when using a file on a shared directory.
logmgr = LogManager(log_filename, "w", comm)
add_run_info(logmgr)
add_general_quantities(logmgr)
log_quantities =\
{"rank_data_swap_timer": IntervalTimer("rank_data_swap_timer",
"Time spent evaluating RankDataSwapAssign"),
"rank_data_swap_counter": EventCounter("rank_data_swap_counter",
"Number of RankDataSwapAssign instructions evaluated"),
"exec_timer": IntervalTimer("exec_timer",
"Total time spent executing instructions"),
"insn_eval_timer": IntervalTimer("insn_eval_timer",
"Time spend evaluating instructions"),
"future_eval_timer": IntervalTimer("future_eval_timer",
"Time spent evaluating futures"),
"busy_wait_timer": IntervalTimer("busy_wait_timer",
"Time wasted doing busy wait")}
for quantity in log_quantities.values():
logmgr.add_quantity(quantity)
bound_op = bind(vol_discr, op.sym_operator())
def rhs(t, w):
val, rhs.profile_data = bound_op(queue, profile_data=rhs.profile_data,
log_quantities=log_quantities,
t=t, w=w)
return val
rhs.profile_data = {}
dt = 0.04
dt_stepper = set_up_rk4("w", dt, fields, rhs)
logmgr.tick_before()
for event in dt_stepper.run(t_end=dt * num_steps):
if isinstance(event, dt_stepper.StateComputed):
logmgr.tick_after()
logmgr.tick_before()
logmgr.tick_after()
def print_profile_data(data):
print("""execute() for rank %d:
\tInstruction Evaluation: %f%%
\tFuture Evaluation: %f%%
\tBusy Wait: %f%%
\tTotal: %f seconds""" %
(comm.Get_rank(),
data['insn_eval_time'] / data['total_time'] * 100,
data['future_eval_time'] / data['total_time'] * 100,
data['busy_wait_time'] / data['total_time'] * 100,
data['total_time']))
print_profile_data(rhs.profile_data)
logmgr.close()
def main(write_output=True, order=4):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dims = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(-0.5,)*dims,
b=(0.5,)*dims,
nelements_per_axis=(20,)*dims)
discr = DiscretizationCollection(actx, mesh, order=order)
source_center = np.array([0.1, 0.22, 0.33])[:mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
c = sym.If(sym.Comparison(
np.dot(sym_x, sym_x), "<", 0.15),
np.float32(0.1), np.float32(0.2))
from grudge.models.wave import VariableCoefficientWeakWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = VariableCoefficientWeakWaveOperator(c,
discr.dim,
source_f=(
sym.sin(source_omega*sym_t)
* sym.exp(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
from pytools.obj_array import flat_obj_array
fields = flat_obj_array(discr.zeros(actx),
[discr.zeros(actx) for i in range(discr.dim)])
op.check_bc_coverage(mesh)
c_eval = bind(discr, c)(actx)
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(t=t, w=w)
if mesh.dim == 2:
dt = 0.04 * 0.3
elif mesh.dim == 3:
dt = 0.02 * 0.1
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 1
nsteps = int(final_t/dt)
print("dt=%g nsteps=%d" % (dt, nsteps))
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr)
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(u=event.state_component[0]),
time()-t_last_step)
if step % 10 == 0:
vis.write_vtk_file("fld-var-propogation-speed-%04d.vtu" % step,
[
("u", event.state_component[0]),
("v", event.state_component[1:]),
("c", c_eval),
])
t_last_step = time()
def f(x):
return flat_obj_array(
sym.sin(3 * x[1]) + sym.cos(3 * x[0]) + 1.0,
sym.sin(2 * x[0]) + sym.cos(x[1]),
3.0 * sym.cos(x[0] / 2) + sym.cos(x[1]),
)[:ambient_dim]
def main(write_output=True, order=4):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
if mesh_dist.is_mananger_rank():
dims = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(16, ) * dims)
print("%d elements" % mesh.nelements)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
del mesh
else:
local_mesh = mesh_dist.receive_mesh_part()
discr = DGDiscretizationWithBoundaries(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if local_mesh.dim == 2:
dt = 0.04
elif local_mesh.dim == 3:
dt = 0.02
source_center = np.array([0.1, 0.22, 0.33])[:local_mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(local_mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(
-0.1,
discr.dim,
source_f=(
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
from pytools.obj_array import flat_obj_array
fields = flat_obj_array(discr.zeros(actx),
[discr.zeros(actx) for i in range(discr.dim)])
# FIXME
#dt = op.estimate_rk4_timestep(discr, fields=fields)
op.check_bc_coverage(local_mesh)
# print(sym.pretty(op.sym_operator()))
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(t=t, w=w)
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 10
nsteps = int(final_t / dt)
print("dt=%g nsteps=%d" % (dt, nsteps))
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=order)
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
rank = comm.Get_rank()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(u=event.state_component[0]),
time() - t_last_step)
if step % 10 == 0:
vis.write_vtk_file(
"fld-wave-min-mpi-%03d-%04d.vtu" % (
rank,
step,
), [
("u", event.state_component[0]),
("v", event.state_component[1:]),
])
t_last_step = time()
def f(x):
return sym.join_fields(
sym.sin(3 * x[0]) + sym.cos(3 * x[1]),
sym.sin(2 * x[0]) + sym.cos(x[1]))
