def test_wave_stability(actx_factory,
problem,
timestep_scale,
order,
visualize=False):
"""Checks stability of the wave operator for a given problem setup.
Adjust *timestep_scale* to get timestep close to stability limit.
"""
actx = actx_factory()
p = problem
sym_u, sym_v, sym_f, sym_rhs = sym_wave(p.dim, p.sym_phi)
mesh = p.mesh_factory(8)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
def sym_eval(expr, t):
return sym.EvaluationMapper({"c": p.c, "x": nodes, "t": t})(expr)
def get_rhs(t, w):
result = wave_operator(discr, c=p.c, w=w)
result[0] += sym_eval(sym_f, t)
return result
t = 0.
u = sym_eval(sym_u, t)
v = sym_eval(sym_v, t)
fields = flat_obj_array(u, v)
from mirgecom.integrators import rk4_step
dt = timestep_scale / order**2
for istep in range(10):
fields = rk4_step(fields, t, dt, get_rhs)
t += dt
expected_u = sym_eval(sym_u, 10 * dt)
expected_v = sym_eval(sym_v, 10 * dt)
expected_fields = flat_obj_array(expected_u, expected_v)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order)
vis.write_vtk_file("wave_stability.vtu", [
("u", fields[0]),
("v", fields[1:]),
("u_expected", expected_fields[0]),
("v_expected", expected_fields[1:]),
])
err = discr.norm(fields - expected_fields, np.inf)
max_err = discr.norm(expected_fields, np.inf)
assert err < max_err
def main(ctx_factory=cl.create_some_context, use_logmgr=True,
use_leap=False, use_profiling=False, casename=None,
rst_filename=None, actx_class=PyOpenCLArrayContext):
"""Run the example."""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from mpi4py import MPI
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
logmgr = initialize_logmgr(use_logmgr,
filename="heat-source.sqlite", mode="wu", mpi_comm=comm)
if use_profiling:
queue = cl.CommandQueue(
cl_ctx, properties=cl.command_queue_properties.PROFILING_ENABLE)
else:
queue = cl.CommandQueue(cl_ctx)
actx = actx_class(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)))
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
t = 0
t_final = 0.0002
istep = 0
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,
nelements_per_axis=(nel_1d,)*dim,
boundary_tag_to_face={
"dirichlet": ["+x", "-x"],
"neumann": ["+y", "-y"]
}
)
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()
order = 3
discr = EagerDGDiscretization(actx, local_mesh, order=order,
mpi_communicator=comm)
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.0025/(nel_1d*order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
source_width = 0.2
from arraycontext import thaw
nodes = thaw(discr.nodes(), actx)
boundaries = {
DTAG_BOUNDARY("dirichlet"): DirichletDiffusionBoundary(0.),
DTAG_BOUNDARY("neumann"): NeumannDiffusionBoundary(0.)
}
u = discr.zeros(actx)
if logmgr:
logmgr_add_device_name(logmgr, queue)
logmgr_add_device_memory_usage(logmgr, queue)
logmgr.add_watches(["step.max", "t_step.max", "t_log.max"])
try:
logmgr.add_watches(["memory_usage_python.max", "memory_usage_gpu.max"])
except KeyError:
pass
if use_profiling:
logmgr.add_watches(["multiply_time.max"])
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
vis = make_visualizer(discr)
def rhs(t, u):
return (
diffusion_operator(
discr, quad_tag=DISCR_TAG_BASE,
alpha=1, boundaries=boundaries, u=u)
+ actx.np.exp(-np.dot(nodes, nodes)/source_width**2))
compiled_rhs = actx.compile(rhs)
rank = comm.Get_rank()
while t < t_final:
if logmgr:
logmgr.tick_before()
if istep % 10 == 0:
print(istep, t, actx.to_numpy(actx.np.linalg.norm(u[0])))
vis.write_vtk_file("fld-heat-source-mpi-%03d-%04d.vtu" % (rank, istep),
[
("u", u)
], overwrite=True)
u = rk4_step(u, t, dt, compiled_rhs)
t += dt
istep += 1
if logmgr:
set_dt(logmgr, dt)
logmgr.tick_after()
final_answer = discr.norm(u, np.inf)
resid = abs(final_answer - 0.00020620711665201585)
if resid > 1e-15:
raise ValueError(f"Run did not produce the expected result {resid=}")
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
from mpi4py import MPI
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
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=(nel_1d, ) * dim,
boundary_tag_to_face={
"dirichlet": ["+x", "-x"],
"neumann": ["+y", "-y"]
})
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()
order = 3
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.0025 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
source_width = 0.2
nodes = thaw(actx, discr.nodes())
u = discr.zeros(actx)
vis = make_visualizer(discr, order + 3 if dim == 2 else order)
boundaries = {
grudge_sym.DTAG_BOUNDARY("dirichlet"): DirichletDiffusionBoundary(0.),
grudge_sym.DTAG_BOUNDARY("neumann"): NeumannDiffusionBoundary(0.)
}
def rhs(t, u):
return (
diffusion_operator(discr, alpha=1, boundaries=boundaries, u=u) +
actx.np.exp(-np.dot(nodes, nodes) / source_width**2))
rank = comm.Get_rank()
t = 0
t_final = 0.01
istep = 0
while True:
if istep % 10 == 0:
print(istep, t, discr.norm(u))
vis.write_vtk_file(
"fld-heat-source-mpi-%03d-%04d.vtu" % (rank, istep),
[("u", u)])
if t >= t_final:
break
u = rk4_step(u, t, dt, rhs)
t += dt
istep += 1
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
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=(nel_1d, ) * dim)
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()
order = 3
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.75 / (nel_1d * order**2)
elif dim == 3:
# no deep meaning here, just a fudge factor
dt = 0.45 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
fields = flat_obj_array(bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)])
vis = make_visualizer(discr, order + 3 if dim == 2 else order)
def rhs(t, w):
return wave_operator(discr, c=1, w=w)
rank = comm.Get_rank()
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
if istep % 10 == 0:
print(istep, t, discr.norm(fields[0]))
vis.write_vtk_file(
"fld-wave-eager-mpi-%03d-%04d.vtu" % (rank, istep), [
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
def _euler_flow_stepper(actx, parameters):
"""
Implements a generic time stepping loop for testing an inviscid flow.
"""
logging.basicConfig(format="%(message)s", level=logging.INFO)
mesh = parameters["mesh"]
t = parameters["time"]
order = parameters["order"]
t_final = parameters["tfinal"]
initializer = parameters["initializer"]
exittol = parameters["exittol"]
casename = parameters["casename"]
boundaries = parameters["boundaries"]
eos = parameters["eos"]
cfl = parameters["cfl"]
dt = parameters["dt"]
constantcfl = parameters["constantcfl"]
nstepstatus = parameters["nstatus"]
if t_final <= t:
return (0.0)
rank = 0
dim = mesh.dim
istep = 0
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
fields = initializer(0, nodes)
sdt = get_inviscid_timestep(discr, eos=eos, cfl=cfl, q=fields)
initname = initializer.__class__.__name__
eosname = eos.__class__.__name__
message = (f"Num {dim}d order-{order} elements: {mesh.nelements}\n"
f"Timestep: {dt}\n"
f"Final time: {t_final}\n"
f"Status freq: {nstepstatus}\n"
f"Initialization: {initname}\n"
f"EOS: {eosname}")
logger.info(message)
vis = make_visualizer(discr, discr.order + 3 if dim == 2 else discr.order)
def write_soln(write_status=True):
cv = split_conserved(dim, fields)
dv = eos.dependent_vars(cv)
expected_result = initializer(t, nodes)
result_resid = fields - expected_result
maxerr = [
np.max(np.abs(result_resid[i].get())) for i in range(dim + 2)
]
mindv = [np.min(dvfld.get()) for dvfld in dv]
maxdv = [np.max(dvfld.get()) for dvfld in dv]
if write_status is True:
statusmsg = (f"Status: Step({istep}) Time({t})\n"
f"------ P({mindv[0]},{maxdv[0]})\n"
f"------ T({mindv[1]},{maxdv[1]})\n"
f"------ dt,cfl = ({dt},{cfl})\n"
f"------ Err({maxerr})")
logger.info(statusmsg)
io_fields = ["cv", split_conserved(dim, fields)]
io_fields += eos.split_fields(dim, dv)
io_fields.append(("exact_soln", expected_result))
io_fields.append(("residual", result_resid))
nameform = casename + "-{iorank:04d}-{iostep:06d}.vtu"
visfilename = nameform.format(iorank=rank, iostep=istep)
vis.write_vtk_file(visfilename, io_fields)
return maxerr
def rhs(t, q):
return inviscid_operator(discr,
eos=eos,
boundaries=boundaries,
q=q,
t=t)
while t < t_final:
if constantcfl is True:
dt = sdt
else:
cfl = dt / sdt
if nstepstatus > 0:
if istep % nstepstatus == 0:
write_soln()
fields = rk4_step(fields, t, dt, rhs)
t += dt
istep += 1
sdt = get_inviscid_timestep(discr, eos=eos, cfl=cfl, q=fields)
if nstepstatus > 0:
logger.info("Writing final dump.")
maxerr = max(write_soln(False))
else:
expected_result = initializer(t, nodes)
maxerr = discr.norm(fields - expected_result, np.inf)
logger.info(f"Max Error: {maxerr}")
if maxerr > exittol:
raise ValueError("Solution failed to follow expected result.")
return (maxerr)
def test_diffusion_discontinuous_alpha(actx_factory, order, visualize=False):
"""
Checks the accuracy of the diffusion operator for an alpha field that has a
jump across an element face.
"""
actx = actx_factory()
n = 8
mesh = get_box_mesh(1, -1, 1, n)
from grudge.eager import EagerDGDiscretization
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
# Set up a 1D heat equation interface problem, apply the diffusion operator to
# the exact steady state solution, and check that it's zero
lower_mask_np = np.empty((n, order + 1), dtype=int)
lower_mask_np[:, :] = 0
lower_mask_np[:int(n / 2), :] = 1
lower_mask = DOFArray(actx, (actx.from_numpy(lower_mask_np), ))
upper_mask_np = np.empty((n, order + 1), dtype=int)
upper_mask_np[:, :] = 0
upper_mask_np[int(n / 2):, :] = 1
upper_mask = DOFArray(actx, (actx.from_numpy(upper_mask_np), ))
alpha_lower = 0.5
alpha_upper = 1
alpha = alpha_lower * lower_mask + alpha_upper * upper_mask
boundaries = {
DTAG_BOUNDARY("-0"): DirichletDiffusionBoundary(0.),
DTAG_BOUNDARY("+0"): DirichletDiffusionBoundary(1.),
}
flux = -alpha_lower * alpha_upper / (alpha_lower + alpha_upper)
u_steady = (
-flux / alpha_lower * (nodes[0] + 1) * lower_mask # noqa: E126, E221
+ (1 - flux / alpha_upper * (nodes[0] - 1)) * upper_mask) # noqa: E131
def get_rhs(t, u):
return diffusion_operator(discr,
quad_tag=DISCR_TAG_BASE,
alpha=alpha,
boundaries=boundaries,
u=u)
rhs = get_rhs(0, u_steady)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order + 3)
vis.write_vtk_file(
"diffusion_discontinuous_alpha_rhs_{order}.vtu".format(
order=order), [
("alpha", alpha),
("u_steady", u_steady),
("rhs", rhs),
])
linf_err = discr.norm(rhs, np.inf)
assert (linf_err < 1e-11)
# Now check stability
from numpy.random import rand
perturb_np = np.empty((n, order + 1), dtype=float)
for i in range(n):
perturb_np[i, :] = 0.1 * (rand() - 0.5)
perturb = DOFArray(actx, (actx.from_numpy(perturb_np), ))
u = u_steady + perturb
dt = 1e-3 / order**2
t = 0
from mirgecom.integrators import rk4_step
for _ in range(50):
u = rk4_step(u, t, dt, get_rhs)
t += dt
if visualize:
vis.write_vtk_file(
"diffusion_disc_alpha_stability_{order}.vtu".format(order=order), [
("alpha", alpha),
("u", u),
("u_steady", u_steady),
])
linf_diff = discr.norm(u - u_steady, np.inf)
assert linf_diff < 0.1
def main(snapshot_pattern="wave-eager-{step:04d}-{rank:04d}.pkl",
restart_step=None):
"""Drive the example."""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
num_parts = comm.Get_size()
if restart_step is None:
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
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,
nelements_per_axis=(nel_1d, ) *
dim)
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()
fields = None
else:
from mirgecom.restart import read_restart_data
restart_data = read_restart_data(
actx, snapshot_pattern.format(step=restart_step, rank=rank))
local_mesh = restart_data["local_mesh"]
nel_1d = restart_data["nel_1d"]
assert comm.Get_size() == restart_data["num_parts"]
order = 3
discr = EagerDGDiscretization(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if local_mesh.dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.7 / (nel_1d * order**2)
elif dim == 3:
# no deep meaning here, just a fudge factor
dt = 0.4 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
t_final = 3
if restart_step is None:
t = 0
istep = 0
fields = flat_obj_array(bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)])
else:
t = restart_data["t"]
istep = restart_step
assert istep == restart_step
restart_fields = restart_data["fields"]
old_order = restart_data["order"]
if old_order != order:
old_discr = EagerDGDiscretization(actx,
local_mesh,
order=old_order,
mpi_communicator=comm)
from meshmode.discretization.connection import make_same_mesh_connection
connection = make_same_mesh_connection(
actx, discr.discr_from_dd("vol"),
old_discr.discr_from_dd("vol"))
fields = connection(restart_fields)
else:
fields = restart_fields
vis = make_visualizer(discr)
def rhs(t, w):
return wave_operator(discr, c=1, w=w)
while t < t_final:
# restart must happen at beginning of step
if istep % 100 == 0 and (
# Do not overwrite the restart file that we just read.
istep != restart_step):
from mirgecom.restart import write_restart_file
write_restart_file(actx,
restart_data={
"local_mesh": local_mesh,
"order": order,
"fields": fields,
"t": t,
"step": istep,
"nel_1d": nel_1d,
"num_parts": num_parts
},
filename=snapshot_pattern.format(step=istep,
rank=rank),
comm=comm)
if istep % 10 == 0:
print(istep, t, discr.norm(fields[0]))
vis.write_parallel_vtk_file(
comm, "fld-wave-eager-mpi-%03d-%04d.vtu" % (rank, istep), [
("u", fields[0]),
("v", fields[1:]),
])
fields = rk4_step(fields, t, dt, rhs)
t += dt
istep += 1
def test_diffusion_accuracy(actx_factory,
problem,
nsteps,
dt,
scales,
order,
visualize=False):
"""
Checks the accuracy of the diffusion operator by solving the heat equation for a
given problem setup.
"""
actx = actx_factory()
p = problem
sym_diffusion_u = sym_diffusion(p.dim, p.sym_alpha, p.sym_u)
# In order to support manufactured solutions, we modify the heat equation
# to add a source term f. If the solution is exact, this term should be 0.
sym_t = pmbl.var("t")
sym_f = sym.diff(sym_t)(p.sym_u) - sym_diffusion_u
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in scales:
mesh = p.get_mesh(n)
from grudge.eager import EagerDGDiscretization
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory, \
PolynomialWarpAndBlendGroupFactory
discr = EagerDGDiscretization(
actx,
mesh,
discr_tag_to_group_factory={
DISCR_TAG_BASE: PolynomialWarpAndBlendGroupFactory(order),
DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(3 * order),
})
nodes = thaw(actx, discr.nodes())
def sym_eval(expr, t):
return sym.EvaluationMapper({"x": nodes, "t": t})(expr)
alpha = sym_eval(p.sym_alpha, 0.)
if isinstance(alpha, DOFArray):
discr_tag = DISCR_TAG_QUAD
else:
discr_tag = DISCR_TAG_BASE
def get_rhs(t, u):
return (
diffusion_operator(discr,
quad_tag=discr_tag,
alpha=alpha,
boundaries=p.get_boundaries(discr, actx, t),
u=u) + sym_eval(sym_f, t))
t = 0.
u = sym_eval(p.sym_u, t)
from mirgecom.integrators import rk4_step
for _ in range(nsteps):
u = rk4_step(u, t, dt, get_rhs)
t += dt
expected_u = sym_eval(p.sym_u, t)
rel_linf_err = (discr.norm(u - expected_u, np.inf) /
discr.norm(expected_u, np.inf))
eoc_rec.add_data_point(1. / n, rel_linf_err)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, discr.order + 3)
vis.write_vtk_file(
"diffusion_accuracy_{order}_{n}.vtu".format(order=order, n=n),
[
("u", u),
("expected_u", expected_u),
])
print("L^inf error:")
print(eoc_rec)
# Expected convergence rates from Hesthaven/Warburton book
expected_order = order + 1 if order % 2 == 0 else order
assert (eoc_rec.order_estimate() >= expected_order - 0.5
or eoc_rec.max_error() < 1e-11)
def _euler_flow_stepper(actx, parameters):
logging.basicConfig(format="%(message)s", level=logging.INFO)
mesh = parameters["mesh"]
t = parameters["time"]
order = parameters["order"]
t_final = parameters["tfinal"]
initializer = parameters["initializer"]
exittol = parameters["exittol"]
casename = parameters["casename"]
boundaries = parameters["boundaries"]
eos = parameters["eos"]
cfl = parameters["cfl"]
dt = parameters["dt"]
constantcfl = parameters["constantcfl"]
nstepstatus = parameters["nstatus"]
if t_final <= t:
return (0.0)
rank = 0
dim = mesh.dim
istep = 0
discr = EagerDGDiscretization(actx, mesh, order=order)
nodes = thaw(actx, discr.nodes())
cv = initializer(nodes)
sdt = cfl * get_inviscid_timestep(discr, eos=eos, cv=cv)
initname = initializer.__class__.__name__
eosname = eos.__class__.__name__
logger.info(f"Num {dim}d order-{order} elements: {mesh.nelements}\n"
f"Timestep: {dt}\n"
f"Final time: {t_final}\n"
f"Status freq: {nstepstatus}\n"
f"Initialization: {initname}\n"
f"EOS: {eosname}")
vis = make_visualizer(discr, order)
def write_soln(state, write_status=True):
dv = eos.dependent_vars(cv=state)
expected_result = initializer(nodes, t=t)
result_resid = (state - expected_result).join()
maxerr = [
np.max(np.abs(result_resid[i].get())) for i in range(dim + 2)
]
mindv = [np.min(dvfld.get()) for dvfld in dv]
maxdv = [np.max(dvfld.get()) for dvfld in dv]
if write_status is True:
statusmsg = (f"Status: Step({istep}) Time({t})\n"
f"------ P({mindv[0]},{maxdv[0]})\n"
f"------ T({mindv[1]},{maxdv[1]})\n"
f"------ dt,cfl = ({dt},{cfl})\n"
f"------ Err({maxerr})")
logger.info(statusmsg)
io_fields = ["cv", state]
io_fields += eos.split_fields(dim, dv)
io_fields.append(("exact_soln", expected_result))
io_fields.append(("residual", result_resid))
nameform = casename + "-{iorank:04d}-{iostep:06d}.vtu"
visfilename = nameform.format(iorank=rank, iostep=istep)
vis.write_vtk_file(visfilename, io_fields)
return maxerr
def rhs(t, q):
return euler_operator(discr,
eos=eos,
boundaries=boundaries,
cv=q,
time=t)
filter_order = 8
eta = .5
alpha = -1.0 * np.log(np.finfo(float).eps)
nummodes = int(1)
for _ in range(dim):
nummodes *= int(order + dim + 1)
nummodes /= math.factorial(int(dim))
cutoff = int(eta * order)
from mirgecom.filter import (exponential_mode_response_function as xmrfunc,
filter_modally)
frfunc = partial(xmrfunc, alpha=alpha, filter_order=filter_order)
while t < t_final:
if constantcfl is True:
dt = sdt
else:
cfl = dt / sdt
if nstepstatus > 0:
if istep % nstepstatus == 0:
write_soln(state=cv)
cv = rk4_step(cv, t, dt, rhs)
cv = make_conserved(dim,
q=filter_modally(discr, "vol", cutoff, frfunc,
cv.join()))
t += dt
istep += 1
sdt = cfl * get_inviscid_timestep(discr, eos=eos, cv=cv)
if nstepstatus > 0:
logger.info("Writing final dump.")
maxerr = max(write_soln(cv, False))
else:
expected_result = initializer(nodes, time=t)
maxerr = discr.norm((cv - expected_result).join(), np.inf)
logger.info(f"Max Error: {maxerr}")
if maxerr > exittol:
raise ValueError("Solution failed to follow expected result.")
return (maxerr)
def main(use_profiling=False, use_logmgr=False, lazy_eval: bool = False):
"""Drive the example."""
cl_ctx = cl.create_some_context()
logmgr = initialize_logmgr(use_logmgr, filename="wave.sqlite", mode="wu")
if use_profiling:
if lazy_eval:
raise RuntimeError("Cannot run lazy with profiling.")
queue = cl.CommandQueue(
cl_ctx, properties=cl.command_queue_properties.PROFILING_ENABLE)
actx = PyOpenCLProfilingArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)))
else:
queue = cl.CommandQueue(cl_ctx)
if lazy_eval:
actx = PytatoPyOpenCLArrayContext(queue)
else:
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
dim = 2
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 3
discr = EagerDGDiscretization(actx, mesh, order=order)
current_cfl = 0.485
wave_speed = 1.0
from grudge.dt_utils import characteristic_lengthscales
nodal_dt = characteristic_lengthscales(actx, discr) / wave_speed
from grudge.op import nodal_min
dt = actx.to_numpy(current_cfl * nodal_min(discr, "vol", nodal_dt))[()]
print("%d elements" % mesh.nelements)
fields = flat_obj_array(bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)])
if logmgr:
logmgr_add_cl_device_info(logmgr, queue)
logmgr_add_device_memory_usage(logmgr, queue)
logmgr.add_watches(["step.max", "t_step.max", "t_log.max"])
try:
logmgr.add_watches(
["memory_usage_python.max", "memory_usage_gpu.max"])
except KeyError:
pass
if use_profiling:
logmgr.add_watches(["multiply_time.max"])
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
vis = make_visualizer(discr)
def rhs(t, w):
return wave_operator(discr, c=wave_speed, w=w)
compiled_rhs = actx.compile(rhs)
t = 0
t_final = 1
istep = 0
while t < t_final:
if logmgr:
logmgr.tick_before()
fields = thaw(freeze(fields, actx), actx)
fields = rk4_step(fields, t, dt, compiled_rhs)
if istep % 10 == 0:
if use_profiling:
print(actx.tabulate_profiling_data())
print(istep, t, actx.to_numpy(discr.norm(fields[0], np.inf)))
vis.write_vtk_file("fld-wave-%04d.vtu" % istep, [
("u", fields[0]),
("v", fields[1:]),
],
overwrite=True)
t += dt
istep += 1
if logmgr:
set_dt(logmgr, dt)
logmgr.tick_after()
def main(snapshot_pattern="wave-mpi-{step:04d}-{rank:04d}.pkl", restart_step=None,
use_profiling=False, use_logmgr=False, actx_class=PyOpenCLArrayContext):
"""Drive the example."""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from mpi4py import MPI
comm = MPI.COMM_WORLD
rank = comm.Get_rank()
num_parts = comm.Get_size()
logmgr = initialize_logmgr(use_logmgr,
filename="wave-mpi.sqlite", mode="wu", mpi_comm=comm)
if use_profiling:
queue = cl.CommandQueue(cl_ctx,
properties=cl.command_queue_properties.PROFILING_ENABLE)
actx = actx_class(queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
logmgr=logmgr)
else:
queue = cl.CommandQueue(cl_ctx)
actx = actx_class(queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)))
if restart_step is None:
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
nel_1d = 16
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,
nelements_per_axis=(nel_1d,)*dim)
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()
fields = None
else:
from mirgecom.restart import read_restart_data
restart_data = read_restart_data(
actx, snapshot_pattern.format(step=restart_step, rank=rank)
)
local_mesh = restart_data["local_mesh"]
nel_1d = restart_data["nel_1d"]
assert comm.Get_size() == restart_data["num_parts"]
order = 3
discr = EagerDGDiscretization(actx, local_mesh, order=order,
mpi_communicator=comm)
current_cfl = 0.485
wave_speed = 1.0
from grudge.dt_utils import characteristic_lengthscales
dt = current_cfl * characteristic_lengthscales(actx, discr) / wave_speed
from grudge.op import nodal_min
dt = nodal_min(discr, "vol", dt)
t_final = 1
if restart_step is None:
t = 0
istep = 0
fields = flat_obj_array(
bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)]
)
else:
t = restart_data["t"]
istep = restart_step
assert istep == restart_step
restart_fields = restart_data["fields"]
old_order = restart_data["order"]
if old_order != order:
old_discr = EagerDGDiscretization(actx, local_mesh, order=old_order,
mpi_communicator=comm)
from meshmode.discretization.connection import make_same_mesh_connection
connection = make_same_mesh_connection(actx, discr.discr_from_dd("vol"),
old_discr.discr_from_dd("vol"))
fields = connection(restart_fields)
else:
fields = restart_fields
if logmgr:
logmgr_add_cl_device_info(logmgr, queue)
logmgr_add_device_memory_usage(logmgr, queue)
logmgr.add_watches(["step.max", "t_step.max", "t_log.max"])
try:
logmgr.add_watches(["memory_usage_python.max", "memory_usage_gpu.max"])
except KeyError:
pass
if use_profiling:
logmgr.add_watches(["multiply_time.max"])
vis_timer = IntervalTimer("t_vis", "Time spent visualizing")
logmgr.add_quantity(vis_timer)
vis = make_visualizer(discr)
def rhs(t, w):
return wave_operator(discr, c=wave_speed, w=w)
compiled_rhs = actx.compile(rhs)
while t < t_final:
if logmgr:
logmgr.tick_before()
# restart must happen at beginning of step
if istep % 100 == 0 and (
# Do not overwrite the restart file that we just read.
istep != restart_step):
from mirgecom.restart import write_restart_file
write_restart_file(
actx, restart_data={
"local_mesh": local_mesh,
"order": order,
"fields": fields,
"t": t,
"step": istep,
"nel_1d": nel_1d,
"num_parts": num_parts},
filename=snapshot_pattern.format(step=istep, rank=rank),
comm=comm
)
if istep % 10 == 0:
print(istep, t, discr.norm(fields[0]))
vis.write_parallel_vtk_file(
comm,
"fld-wave-mpi-%03d-%04d.vtu" % (rank, istep),
[
("u", fields[0]),
("v", fields[1:]),
], overwrite=True
)
fields = thaw(freeze(fields, actx), actx)
fields = rk4_step(fields, t, dt, compiled_rhs)
t += dt
istep += 1
if logmgr:
set_dt(logmgr, dt)
logmgr.tick_after()
final_soln = discr.norm(fields[0])
assert np.abs(final_soln - 0.04409852463947439) < 1e-14
def main(use_profiling=False):
"""Drive the example."""
cl_ctx = cl.create_some_context()
if use_profiling:
queue = cl.CommandQueue(
cl_ctx, properties=cl.command_queue_properties.PROFILING_ENABLE)
actx = PyOpenCLProfilingArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)))
else:
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue,
allocator=cl_tools.MemoryPool(
cl_tools.ImmediateAllocator(queue)))
dim = 2
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(nel_1d, ) * dim)
order = 3
if dim == 2:
# no deep meaning here, just a fudge factor
dt = 0.7 / (nel_1d * order**2)
elif dim == 3:
# no deep meaning here, just a fudge factor
dt = 0.4 / (nel_1d * order**2)
else:
raise ValueError("don't have a stable time step guesstimate")
print("%d elements" % mesh.nelements)
discr = EagerDGDiscretization(actx, mesh, order=order)
fields = flat_obj_array(bump(actx, discr),
[discr.zeros(actx) for i in range(discr.dim)])
vis = make_visualizer(discr)
def rhs(t, w):
return wave_operator(discr, c=1, w=w)
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
if istep % 10 == 0:
if use_profiling:
print(actx.tabulate_profiling_data())
print(istep, t, discr.norm(fields[0], np.inf))
vis.write_vtk_file("fld-wave-eager-%04d.vtu" % istep, [
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
