def test_norm_obj_array(actx_factory, p):
"""Test :func:`grudge.op.norm` for object arrays."""
actx = actx_factory()
dim = 2
mesh = mgen.generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(8, ) * dim,
order=1)
dcoll = DiscretizationCollection(actx, mesh, order=4)
w = make_obj_array([1.0, 2.0, 3.0])[:dim]
# {{ scalar
norm = op.norm(dcoll, w[0], p)
norm_exact = w[0]
logger.info("norm: %.5e %.5e", norm, norm_exact)
assert abs(norm - norm_exact) < 1.0e-14
# }}}
# {{{ vector
norm = op.norm(dcoll, w, p)
norm_exact = np.sqrt(np.sum(w**2)) if p == 2 else np.max(w)
logger.info("norm: %.5e %.5e", norm, norm_exact)
assert abs(norm - norm_exact) < 1.0e-14
def test_mass_operator_inverse(actx_factory, name):
actx = actx_factory()
# {{{ cases
import mesh_data
if name == "2-1-ellipse":
# curve
builder = mesh_data.EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
elif name == "spheroid":
# surface
builder = mesh_data.SpheroidMeshBuilder()
elif name.startswith("warped_rect"):
builder = mesh_data.WarpedRectMeshBuilder(dim=int(name[-1]))
else:
raise ValueError("unknown geometry name: %s" % name)
# }}}
# {{{ inv(m) @ m == id
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for resolution in builder.resolutions:
mesh = builder.get_mesh(resolution, builder.mesh_order)
dcoll = DiscretizationCollection(actx, mesh, order=builder.order)
volume_discr = dcoll.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume_discr.ndofs)
logger.info("nelements: %d", volume_discr.mesh.nelements)
# {{{ compute inverse mass
def f(x):
return actx.np.cos(4.0 * x[0])
dd = dof_desc.DD_VOLUME
x_volm = thaw(volume_discr.nodes(), actx)
f_volm = f(x_volm)
f_inv = op.inverse_mass(dcoll, op.mass(dcoll, dd, f_volm))
inv_error = actx.to_numpy(
op.norm(dcoll, f_volm - f_inv, 2) / op.norm(dcoll, f_volm, 2))
# }}}
# compute max element size
from grudge.dt_utils import h_max_from_volume
h_max = h_max_from_volume(dcoll)
eoc.add_data_point(h_max, inv_error)
logger.info("inverse mass error\n%s", str(eoc))
# NOTE: both cases give 1.0e-16-ish at the moment, but just to be on the
# safe side, choose a slightly larger tolerance
assert eoc.max_error() < 1.0e-14
def test_trace_pair(actx_factory):
"""Simple smoke test for :class:`grudge.trace_pair.TracePair`."""
actx = actx_factory()
dim = 3
order = 1
n = 4
mesh = mgen.generate_regular_rect_mesh(
a=(-1,)*dim, b=(1,)*dim,
nelements_per_axis=(n,)*dim)
dcoll = DiscretizationCollection(actx, mesh, order=order)
def rand():
return DOFArray(
actx,
tuple(actx.from_numpy(
np.random.rand(grp.nelements, grp.nunit_dofs))
for grp in dcoll.discr_from_dd("vol").groups))
interior = rand()
exterior = rand()
tpair = TracePair("vol", interior=interior, exterior=exterior)
import grudge.op as op
assert op.norm(dcoll, tpair.avg - 0.5*(exterior + interior), np.inf) == 0
assert op.norm(dcoll, tpair.diff - (exterior - interior), np.inf) == 0
assert op.norm(dcoll, tpair.int - interior, np.inf) == 0
assert op.norm(dcoll, tpair.ext - exterior, np.inf) == 0
def test_bessel(actx_factory):
actx = actx_factory()
dims = 2
mesh = mgen.generate_regular_rect_mesh(a=(0.1, ) * dims,
b=(1.0, ) * dims,
nelements_per_axis=(8, ) * dims)
dcoll = DiscretizationCollection(actx, mesh, order=3)
nodes = thaw(dcoll.nodes(), actx)
r = actx.np.sqrt(nodes[0]**2 + nodes[1]**2)
# FIXME: Bessel functions need to brought out of the symbolic
# layer. Related issue: https://github.com/inducer/grudge/issues/93
def bessel_j(actx, n, r):
from grudge import sym, bind
return bind(dcoll, sym.bessel_j(n, sym.var("r")))(actx, r=r)
# https://dlmf.nist.gov/10.6.1
n = 3
bessel_zero = (bessel_j(actx, n + 1, r) + bessel_j(actx, n - 1, r) -
2 * n / r * bessel_j(actx, n, r))
z = op.norm(dcoll, bessel_zero, 2)
assert z < 1e-15
def conv_test(descr, use_quad):
logger.info("-" * 75)
logger.info(descr)
logger.info("-" * 75)
eoc_rec = EOCRecorder()
if use_quad:
qtag = dof_desc.DISCR_TAG_QUAD
else:
qtag = None
ns = [20, 25]
for n in ns:
mesh = mgen.generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
nelements_per_axis=(n, ) *
dims,
order=order)
if use_quad:
discr_tag_to_group_factory = {
qtag: QuadratureSimplexGroupFactory(order=4 * order)
}
else:
discr_tag_to_group_factory = {}
dcoll = DiscretizationCollection(
actx,
mesh,
order=order,
discr_tag_to_group_factory=discr_tag_to_group_factory)
nodes = thaw(dcoll.nodes(), actx)
def zero_inflow(dtag, t=0):
dd = dof_desc.DOFDesc(dtag, qtag)
return dcoll.discr_from_dd(dd).zeros(actx)
adv_op = VariableCoefficientAdvectionOperator(
dcoll,
flat_obj_array(-1 * nodes[1], nodes[0]),
inflow_u=lambda t: zero_inflow(BTAG_ALL, t=t),
flux_type="upwind",
quad_tag=qtag)
total_error = op.norm(dcoll,
adv_op.operator(0, gaussian_mode(nodes)), 2)
eoc_rec.add_data_point(1.0 / n, actx.to_numpy(total_error))
logger.info(
"\n%s",
eoc_rec.pretty_print(abscissa_label="h", error_label="L2 Error"))
return eoc_rec.order_estimate(), np.array(
[x[1] for x in eoc_rec.history])
def test_elementwise_reductions(actx_factory):
actx = actx_factory()
from mesh_data import BoxMeshBuilder
builder = BoxMeshBuilder(ambient_dim=1)
nelements = 4
mesh = builder.get_mesh(nelements, builder.mesh_order)
dcoll = DiscretizationCollection(actx, mesh, order=builder.order)
x = thaw(dcoll.nodes(), actx)
def f(x):
return actx.np.sin(x[0])
field = f(x)
mins = []
maxs = []
sums = []
for grp_f in field:
min_res = np.empty(grp_f.shape)
max_res = np.empty(grp_f.shape)
sum_res = np.empty(grp_f.shape)
for eidx in range(dcoll.mesh.nelements):
element_data = actx.to_numpy(grp_f[eidx])
min_res[eidx, :] = np.min(element_data)
max_res[eidx, :] = np.max(element_data)
sum_res[eidx, :] = np.sum(element_data)
mins.append(actx.from_numpy(min_res))
maxs.append(actx.from_numpy(max_res))
sums.append(actx.from_numpy(sum_res))
ref_mins = DOFArray(actx, data=tuple(mins))
ref_maxs = DOFArray(actx, data=tuple(maxs))
ref_sums = DOFArray(actx, data=tuple(sums))
elem_mins = op.elementwise_min(dcoll, field)
elem_maxs = op.elementwise_max(dcoll, field)
elem_sums = op.elementwise_sum(dcoll, field)
assert actx.to_numpy(op.norm(dcoll, elem_mins - ref_mins, np.inf)) < 1.e-15
assert actx.to_numpy(op.norm(dcoll, elem_maxs - ref_maxs, np.inf)) < 1.e-15
assert actx.to_numpy(op.norm(dcoll, elem_sums - ref_sums, np.inf)) < 1.e-15
def test_nodal_reductions_with_container(actx_factory):
actx = actx_factory()
from mesh_data import BoxMeshBuilder
builder = BoxMeshBuilder(ambient_dim=2)
mesh = builder.get_mesh(4, builder.mesh_order)
dcoll = DiscretizationCollection(actx, mesh, order=builder.order)
x = thaw(dcoll.nodes(), actx)
def f(x):
return -actx.np.sin(10 * x[0]) * actx.np.cos(2 * x[1])
def g(x):
return actx.np.cos(2 * x[0]) * actx.np.sin(10 * x[1])
def h(x):
return -actx.np.tan(5 * x[0]) * actx.np.tan(0.5 * x[1])
mass = f(x) + g(x)
momentum = make_obj_array([f(x) / g(x), h(x)])
enthalpy = h(x) - g(x)
ary_container = MyContainer(name="container",
mass=mass,
momentum=momentum,
enthalpy=enthalpy)
mass_ref = actx.to_numpy(flatten(mass))
momentum_ref = np.concatenate(
[actx.to_numpy(mom_i) for mom_i in flatten(momentum)])
enthalpy_ref = actx.to_numpy(flatten(enthalpy))
concat_fields = np.concatenate([mass_ref, momentum_ref, enthalpy_ref])
for grudge_op, np_op in [(op.nodal_sum, np.sum), (op.nodal_max, np.max),
(op.nodal_min, np.min)]:
assert np.isclose(actx.to_numpy(grudge_op(dcoll, "vol",
ary_container)),
np_op(concat_fields),
rtol=1e-13)
# Check norm reduction
assert np.isclose(actx.to_numpy(op.norm(dcoll, ary_container, np.inf)),
np.linalg.norm(concat_fields, ord=np.inf),
rtol=1e-13)
def test_norm_complex(actx_factory, p):
actx = actx_factory()
dim = 2
mesh = mgen.generate_regular_rect_mesh(a=(0, ) * dim,
b=(1, ) * dim,
nelements_per_axis=(8, ) * dim,
order=1)
dcoll = DiscretizationCollection(actx, mesh, order=4)
nodes = thaw(dcoll.nodes(), actx)
norm = op.norm(dcoll, (1 + 1j) * nodes[0], p)
if p == 2:
ref_norm = (2 / 3)**0.5
elif p == np.inf:
ref_norm = 2**0.5
logger.info("norm: %.5e %.5e", norm, ref_norm)
assert abs(norm - ref_norm) / abs(ref_norm) < 1e-13
def test_convergence_advec(actx_factory,
mesh_name,
mesh_pars,
op_type,
flux_type,
order,
visualize=False):
"""Test whether 2D advection actually converges"""
actx = actx_factory()
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for mesh_par in mesh_pars:
if mesh_name == "segment":
mesh = mgen.generate_box_mesh([np.linspace(-1.0, 1.0, mesh_par)],
order=order)
dim = 1
dt_factor = 1.0
elif mesh_name == "disk":
pytest.importorskip("meshpy")
from meshpy.geometry import make_circle, GeometryBuilder
from meshpy.triangle import MeshInfo, build
geob = GeometryBuilder()
geob.add_geometry(*make_circle(1))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info = build(mesh_info, max_volume=mesh_par)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
dim = 2
dt_factor = 4
elif mesh_name.startswith("rect"):
dim = int(mesh_name[-1:])
mesh = mgen.generate_regular_rect_mesh(
a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(mesh_par, ) * dim,
order=4)
if dim == 2:
dt_factor = 4
elif dim == 3:
dt_factor = 2
else:
raise ValueError("dt_factor not known for %dd" % dim)
elif mesh_name.startswith("warped"):
dim = int(mesh_name[-1:])
mesh = mgen.generate_warped_rect_mesh(dim,
order=order,
nelements_side=mesh_par)
if dim == 2:
dt_factor = 4
elif dim == 3:
dt_factor = 2
else:
raise ValueError("dt_factor not known for %dd" % dim)
else:
raise ValueError("invalid mesh name: " + mesh_name)
v = np.array([0.27, 0.31, 0.1])[:dim]
norm_v = la.norm(v)
def f(x):
return actx.np.sin(10 * x)
def u_analytic(x, t=0):
return f(-v.dot(x) / norm_v + t * norm_v)
from grudge.models.advection import (StrongAdvectionOperator,
WeakAdvectionOperator)
from meshmode.mesh import BTAG_ALL
dcoll = DiscretizationCollection(actx, mesh, order=order)
op_class = {
"strong": StrongAdvectionOperator,
"weak": WeakAdvectionOperator
}[op_type]
adv_operator = op_class(dcoll,
v,
inflow_u=lambda t: u_analytic(
thaw(dcoll.nodes(dd=BTAG_ALL), actx), t=t),
flux_type=flux_type)
nodes = thaw(dcoll.nodes(), actx)
u = u_analytic(nodes, t=0)
def rhs(t, u):
return adv_operator.operator(t, u)
if dim == 3:
final_time = 0.1
else:
final_time = 0.2
from grudge.dt_utils import h_max_from_volume
h_max = h_max_from_volume(dcoll, dim=dcoll.ambient_dim)
dt = dt_factor * h_max / order**2
nsteps = (final_time // dt) + 1
dt = final_time / nsteps + 1e-15
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
last_u = None
from grudge.shortcuts import make_visualizer
vis = make_visualizer(dcoll)
step = 0
for event in dt_stepper.run(t_end=final_time):
if isinstance(event, dt_stepper.StateComputed):
step += 1
logger.debug("[%04d] t = %.5f", step, event.t)
last_t = event.t
last_u = event.state_component
if visualize:
vis.write_vtk_file("fld-%s-%04d.vtu" % (mesh_par, step),
[("u", event.state_component)])
error_l2 = op.norm(dcoll, last_u - u_analytic(nodes, t=last_t), 2)
logger.info("h_max %.5e error %.5e", h_max, error_l2)
eoc_rec.add_data_point(h_max, actx.to_numpy(error_l2))
logger.info(
"\n%s", eoc_rec.pretty_print(abscissa_label="h",
error_label="L2 Error"))
if mesh_name.startswith("warped"):
# NOTE: curvilinear meshes are hard
assert eoc_rec.order_estimate() > order - 0.5
else:
assert eoc_rec.order_estimate() > order
def main():
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)
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()
order = 3
dcoll = DiscretizationCollection(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, dcoll),
[dcoll.zeros(actx) for i in range(dcoll.dim)])
vis = make_visualizer(dcoll)
def rhs(t, w):
return wave_operator(dcoll, 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:
print(istep, t, op.norm(dcoll, fields[0], p=2))
vis.write_parallel_vtk_file(
comm, f"fld-wave-eager-mpi-{{rank:03d}}-{istep:04d}.vtu", [
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
def main(ctx_factory,
dim=2,
order=4,
use_quad=False,
visualize=False,
flux_type="upwind"):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
force_device_scalars=True,
)
# {{{ parameters
# domain [0, d]^dim
d = 1.0
# number of points in each dimension
npoints = 25
# final time
final_time = 1
if use_quad:
qtag = dof_desc.DISCR_TAG_QUAD
else:
qtag = None
# }}}
# {{{ discretization
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(0, ) * dim,
b=(d, ) * dim,
npoints_per_axis=(npoints, ) * dim,
order=order)
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory
if use_quad:
discr_tag_to_group_factory = {
qtag: QuadratureSimplexGroupFactory(order=4 * order)
}
else:
discr_tag_to_group_factory = {}
from grudge import DiscretizationCollection
dcoll = DiscretizationCollection(
actx,
mesh,
order=order,
discr_tag_to_group_factory=discr_tag_to_group_factory)
# }}}
# {{{ advection operator
# gaussian parameters
def f_halfcircle(x):
source_center = np.array([d / 2, d / 2, d / 2])[:dim]
dist = x - source_center
return ((0.5 + 0.5 * actx.np.tanh(500 *
(-np.dot(dist, dist) + 0.4**2))) *
(0.5 + 0.5 * actx.np.tanh(500 * (dist[0]))))
def zero_inflow_bc(dtag, t=0):
dd = dof_desc.DOFDesc(dtag, qtag)
return dcoll.discr_from_dd(dd).zeros(actx)
from grudge.models.advection import VariableCoefficientAdvectionOperator
x = thaw(dcoll.nodes(), actx)
# velocity field
if dim == 1:
c = x
else:
# solid body rotation
c = flat_obj_array(np.pi * (d / 2 - x[1]), np.pi * (x[0] - d / 2),
0)[:dim]
adv_operator = VariableCoefficientAdvectionOperator(
dcoll,
c,
inflow_u=lambda t: zero_inflow_bc(BTAG_ALL, t),
quad_tag=qtag,
flux_type=flux_type)
u = f_halfcircle(x)
def rhs(t, u):
return adv_operator.operator(t, u)
dt = actx.to_numpy(
adv_operator.estimate_rk4_timestep(actx, dcoll, fields=u))
logger.info("Timestep size: %g", dt)
# }}}
# {{{ time stepping
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
plot = Plotter(actx, dcoll, order, visualize=visualize, ylim=[-0.1, 1.1])
step = 0
for event in dt_stepper.run(t_end=final_time):
if not isinstance(event, dt_stepper.StateComputed):
continue
if step % 10 == 0:
norm_u = actx.to_numpy(op.norm(dcoll, event.state_component, 2))
plot(event, "fld-var-velocity-%04d" % step)
step += 1
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
# NOTE: These are here to ensure the solution is bounded for the
# time interval specified
assert norm_u < 1
FACE_RESTR_INTERIOR, "all_faces",
flux(dcoll, interior_tpair)))
duh_by_dt = op.inverse_mass(dcoll,
np.dot([2 * np.pi], Su) - lift)
# forward euler time step
uh = uh + dt * duh_by_dt
t += dt
# ENDEXAMPLE
# Plot the solution:
def u_exact(x, t):
return actx.np.sin(x[0] - 2 * np.pi * t)
assert op.norm(dcoll,
uh - u_exact(x_vol, t_final),
p=2) <= 0.1
import matplotlib.pyplot as plt
from arraycontext import to_numpy
plt.plot(to_numpy(actx.np.ravel(x_vol[0][0]), actx),
to_numpy(actx.np.ravel(uh[0]), actx), label="Numerical")
plt.plot(to_numpy(actx.np.ravel(x_vol[0][0]), actx),
to_numpy(actx.np.ravel(u_exact(x_vol, t_final)[0]), actx), label="Exact")
plt.xlabel("$x$")
plt.ylabel("$u$")
plt.legend()
plt.show()
def main(ctx_factory, dim=2, order=3, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
force_device_scalars=True,
)
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)
logger.info("%d elements", mesh.nelements)
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory, \
default_simplex_group_factory
dcoll = DiscretizationCollection(
actx, mesh,
discr_tag_to_group_factory={
DISCR_TAG_BASE: default_simplex_group_factory(base_dim=dim, order=order),
DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(3*order),
}
)
# bounded above by 1
c = 0.2 + 0.8*bump(actx, dcoll, center=np.zeros(3), width=0.5)
dt = 0.5 * estimate_rk4_timestep(actx, dcoll, c=1)
fields = flat_obj_array(
bump(actx, dcoll, ),
[dcoll.zeros(actx) for i in range(dcoll.dim)]
)
vis = make_visualizer(dcoll)
def rhs(t, w):
return wave_operator(dcoll, c=c, w=w)
logger.info("dt = %g", dt)
t = 0
t_final = 3
istep = 0
while t < t_final:
fields = rk4_step(fields, t, dt, rhs)
if istep % 10 == 0:
logger.info(f"step: {istep} t: {t} "
f"L2: {op.norm(dcoll, fields[0], 2)} "
f"Linf: {op.norm(dcoll, fields[0], np.inf)} "
f"sol max: {op.nodal_max(dcoll, 'vol', fields[0])} "
f"sol min: {op.nodal_min(dcoll, 'vol', fields[0])}")
if visualize:
vis.write_vtk_file(
f"fld-wave-eager-var-velocity-{istep:04d}.vtu",
[
("c", c),
("u", fields[0]),
("v", fields[1:]),
]
)
t += dt
istep += 1
# NOTE: These are here to ensure the solution is bounded for the
# time interval specified
assert op.norm(dcoll, fields[0], 2) < 1
def norm(self, vec, p=2, dd=None):
return op.norm(self, vec, p, dd)
def main(ctx_factory, dim=2, order=3, visualize=False, lazy=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
if lazy:
actx = PytatoPyOpenCLArrayContext(queue)
else:
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
force_device_scalars=True,
)
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
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)
logger.info("%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()
dcoll = DiscretizationCollection(actx,
local_mesh,
order=order,
mpi_communicator=comm)
fields = WaveState(u=bump(actx, dcoll),
v=make_obj_array(
[dcoll.zeros(actx) for i in range(dcoll.dim)]))
c = 1
dt = actx.to_numpy(0.45 * estimate_rk4_timestep(actx, dcoll, c))
vis = make_visualizer(dcoll)
def rhs(t, w):
return wave_operator(dcoll, c=c, w=w)
compiled_rhs = actx.compile(rhs)
if comm.rank == 0:
logger.info("dt = %g", dt)
import time
start = time.time()
t = 0
t_final = 3
istep = 0
while t < t_final:
if lazy:
fields = thaw(freeze(fields, actx), actx)
fields = rk4_step(fields, t, dt, compiled_rhs)
l2norm = actx.to_numpy(op.norm(dcoll, fields.u, 2))
if istep % 10 == 0:
stop = time.time()
linfnorm = actx.to_numpy(op.norm(dcoll, fields.u, np.inf))
nodalmax = actx.to_numpy(op.nodal_max(dcoll, "vol", fields.u))
nodalmin = actx.to_numpy(op.nodal_min(dcoll, "vol", fields.u))
if comm.rank == 0:
logger.info(f"step: {istep} t: {t} "
f"L2: {l2norm} "
f"Linf: {linfnorm} "
f"sol max: {nodalmax} "
f"sol min: {nodalmin} "
f"wall: {stop-start} ")
if visualize:
vis.write_parallel_vtk_file(
comm, f"fld-wave-eager-mpi-{{rank:03d}}-{istep:04d}.vtu", [
("u", fields.u),
("v", fields.v),
])
start = stop
t += dt
istep += 1
# NOTE: These are here to ensure the solution is bounded for the
# time interval specified
assert l2norm < 1
def test_elementwise_reductions_with_container(actx_factory):
actx = actx_factory()
from mesh_data import BoxMeshBuilder
builder = BoxMeshBuilder(ambient_dim=2)
nelements = 4
mesh = builder.get_mesh(nelements, builder.mesh_order)
dcoll = DiscretizationCollection(actx, mesh, order=builder.order)
x = thaw(dcoll.nodes(), actx)
def f(x):
return actx.np.sin(x[0]) * actx.np.sin(x[1])
def g(x):
return actx.np.cos(x[0]) * actx.np.cos(x[1])
def h(x):
return actx.np.cos(x[0]) * actx.np.sin(x[1])
mass = 2 * f(x) + 0.5 * g(x)
momentum = make_obj_array([f(x) / g(x), h(x)])
enthalpy = 3 * h(x) - g(x)
ary_container = MyContainer(name="container",
mass=mass,
momentum=momentum,
enthalpy=enthalpy)
def _get_ref_data(field):
mins = []
maxs = []
sums = []
for grp_f in field:
min_res = np.empty(grp_f.shape)
max_res = np.empty(grp_f.shape)
sum_res = np.empty(grp_f.shape)
for eidx in range(dcoll.mesh.nelements):
element_data = actx.to_numpy(grp_f[eidx])
min_res[eidx, :] = np.min(element_data)
max_res[eidx, :] = np.max(element_data)
sum_res[eidx, :] = np.sum(element_data)
mins.append(actx.from_numpy(min_res))
maxs.append(actx.from_numpy(max_res))
sums.append(actx.from_numpy(sum_res))
min_field = DOFArray(actx, data=tuple(mins))
max_field = DOFArray(actx, data=tuple(maxs))
sums_field = DOFArray(actx, data=tuple(sums))
return min_field, max_field, sums_field
min_mass, max_mass, sums_mass = _get_ref_data(mass)
min_enthalpy, max_enthalpy, sums_enthalpy = _get_ref_data(enthalpy)
min_mom_x, max_mom_x, sums_mom_x = _get_ref_data(momentum[0])
min_mom_y, max_mom_y, sums_mom_y = _get_ref_data(momentum[1])
min_momentum = make_obj_array([min_mom_x, min_mom_y])
max_momentum = make_obj_array([max_mom_x, max_mom_y])
sums_momentum = make_obj_array([sums_mom_x, sums_mom_y])
reference_min = MyContainer(name="Reference min",
mass=min_mass,
momentum=min_momentum,
enthalpy=min_enthalpy)
reference_max = MyContainer(name="Reference max",
mass=max_mass,
momentum=max_momentum,
enthalpy=max_enthalpy)
reference_sum = MyContainer(name="Reference sums",
mass=sums_mass,
momentum=sums_momentum,
enthalpy=sums_enthalpy)
elem_mins = op.elementwise_min(dcoll, ary_container)
elem_maxs = op.elementwise_max(dcoll, ary_container)
elem_sums = op.elementwise_sum(dcoll, ary_container)
assert actx.to_numpy(op.norm(dcoll, elem_mins - reference_min,
np.inf)) < 1.e-14
assert actx.to_numpy(op.norm(dcoll, elem_maxs - reference_max,
np.inf)) < 1.e-14
assert actx.to_numpy(op.norm(dcoll, elem_sums - reference_sum,
np.inf)) < 1.e-14
def main(ctx_factory, dim=2, order=4, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
force_device_scalars=True,
)
# {{{ parameters
# domain [-d/2, d/2]^dim
d = 1.0
# number of points in each dimension
npoints = 20
# final time
final_time = 1.0
# velocity field
c = np.array([0.5] * dim)
norm_c = la.norm(c)
# flux
flux_type = "central"
# }}}
# {{{ discretization
from meshmode.mesh.generation import generate_box_mesh
mesh = generate_box_mesh(
[np.linspace(-d / 2, d / 2, npoints) for _ in range(dim)], order=order)
from grudge import DiscretizationCollection
dcoll = DiscretizationCollection(actx, mesh, order=order)
# }}}
# {{{ weak advection operator
def f(x):
return actx.np.sin(3 * x)
def u_analytic(x, t=0):
return f(-np.dot(c, x) / norm_c + t * norm_c)
from grudge.models.advection import WeakAdvectionOperator
adv_operator = WeakAdvectionOperator(
dcoll,
c,
inflow_u=lambda t: u_analytic(thaw(dcoll.nodes(dd=BTAG_ALL), actx),
t=t),
flux_type=flux_type)
nodes = thaw(dcoll.nodes(), actx)
u = u_analytic(nodes, t=0)
def rhs(t, u):
return adv_operator.operator(t, u)
dt = actx.to_numpy(
adv_operator.estimate_rk4_timestep(actx, dcoll, fields=u))
logger.info("Timestep size: %g", dt)
# }}}
# {{{ time stepping
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
plot = Plotter(actx, dcoll, order, visualize=visualize, ylim=[-1.1, 1.1])
step = 0
norm_u = 0.0
for event in dt_stepper.run(t_end=final_time):
if not isinstance(event, dt_stepper.StateComputed):
continue
if step % 10 == 0:
norm_u = actx.to_numpy(op.norm(dcoll, event.state_component, 2))
plot(event, "fld-weak-%04d" % step)
step += 1
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
# NOTE: These are here to ensure the solution is bounded for the
# time interval specified
assert norm_u < 1
def test_gradient(actx_factory,
form,
dim,
order,
vectorize,
nested,
visualize=False):
actx = actx_factory()
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for n in [4, 6, 8]:
mesh = mgen.generate_regular_rect_mesh(a=(-1, ) * dim,
b=(1, ) * dim,
nelements_per_axis=(n, ) * dim)
dcoll = DiscretizationCollection(actx, mesh, order=order)
def f(x):
result = dcoll.zeros(actx) + 1
for i in range(dim - 1):
result = result * actx.np.sin(np.pi * x[i])
result = result * actx.np.cos(np.pi / 2 * x[dim - 1])
return result
def grad_f(x):
result = make_obj_array(
[dcoll.zeros(actx) + 1 for _ in range(dim)])
for i in range(dim - 1):
for j in range(i):
result[i] = result[i] * actx.np.sin(np.pi * x[j])
result[i] = result[i] * np.pi * actx.np.cos(np.pi * x[i])
for j in range(i + 1, dim - 1):
result[i] = result[i] * actx.np.sin(np.pi * x[j])
result[i] = result[i] * actx.np.cos(np.pi / 2 * x[dim - 1])
for j in range(dim - 1):
result[dim - 1] = result[dim - 1] * actx.np.sin(np.pi * x[j])
result[dim -
1] = result[dim - 1] * (-np.pi / 2 *
actx.np.sin(np.pi / 2 * x[dim - 1]))
return result
x = thaw(dcoll.nodes(), actx)
if vectorize:
u = make_obj_array([(i + 1) * f(x) for i in range(dim)])
else:
u = f(x)
def get_flux(u_tpair):
dd = u_tpair.dd
dd_allfaces = dd.with_dtag("all_faces")
normal = thaw(dcoll.normal(dd), actx)
u_avg = u_tpair.avg
if vectorize:
if nested:
flux = make_obj_array(
[u_avg_i * normal for u_avg_i in u_avg])
else:
flux = np.outer(u_avg, normal)
else:
flux = u_avg * normal
return op.project(dcoll, dd, dd_allfaces, flux)
dd_allfaces = DOFDesc("all_faces")
if form == "strong":
grad_u = (
op.local_grad(dcoll, u, nested=nested)
# No flux terms because u doesn't have inter-el jumps
)
elif form == "weak":
grad_u = op.inverse_mass(
dcoll,
-op.weak_local_grad(dcoll, u, nested=nested) # pylint: disable=E1130
+ # noqa: W504
op.face_mass(
dcoll,
dd_allfaces,
# Note: no boundary flux terms here because u_ext == u_int == 0
sum(
get_flux(utpair)
for utpair in op.interior_trace_pairs(dcoll, u))))
else:
raise ValueError("Invalid form argument.")
if vectorize:
expected_grad_u = make_obj_array([(i + 1) * grad_f(x)
for i in range(dim)])
if not nested:
expected_grad_u = np.stack(expected_grad_u, axis=0)
else:
expected_grad_u = grad_f(x)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(dcoll,
vis_order=order if dim == 3 else dim + 3)
filename = (
f"test_gradient_{form}_{dim}_{order}"
f"{'_vec' if vectorize else ''}{'_nested' if nested else ''}.vtu"
)
vis.write_vtk_file(filename, [
("u", u),
("grad_u", grad_u),
("expected_grad_u", expected_grad_u),
],
overwrite=True)
rel_linf_err = actx.to_numpy(
op.norm(dcoll, grad_u - expected_grad_u, np.inf) /
op.norm(dcoll, expected_grad_u, np.inf))
eoc_rec.add_data_point(1. / n, rel_linf_err)
print("L^inf error:")
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-11)
def norm(u):
return op.norm(dcoll, u, 2)
def test_surface_divergence_theorem(actx_factory, mesh_name, visualize=False):
r"""Check the surface divergence theorem.
.. math::
\int_Sigma \phi \nabla_i f_i =
\int_\Sigma \nabla_i \phi f_i +
\int_\Sigma \kappa \phi f_i n_i +
\int_{\partial \Sigma} \phi f_i m_i
where :math:`n_i` is the surface normal and :class:`m_i` is the
face normal (which should be orthogonal to both the surface normal
and the face tangent).
"""
actx = actx_factory()
# {{{ cases
if mesh_name == "2-1-ellipse":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
elif mesh_name == "spheroid":
from mesh_data import SpheroidMeshBuilder
builder = SpheroidMeshBuilder()
elif mesh_name == "circle":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=1.0, aspect_ratio=1.0)
elif mesh_name == "starfish":
from mesh_data import StarfishMeshBuilder
builder = StarfishMeshBuilder()
elif mesh_name == "sphere":
from mesh_data import SphereMeshBuilder
builder = SphereMeshBuilder(radius=1.0, mesh_order=16)
else:
raise ValueError("unknown mesh name: %s" % mesh_name)
# }}}
# {{{ convergence
def f(x):
return flat_obj_array(
actx.np.sin(3 * x[1]) + actx.np.cos(3 * x[0]) + 1.0,
actx.np.sin(2 * x[0]) + actx.np.cos(x[1]),
3.0 * actx.np.cos(x[0] / 2) + actx.np.cos(x[1]),
)[:ambient_dim]
from pytools.convergence import EOCRecorder
eoc_global = EOCRecorder()
eoc_local = EOCRecorder()
theta = np.pi / 3.33
ambient_dim = builder.ambient_dim
if ambient_dim == 2:
mesh_rotation = np.array([
[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)],
])
else:
mesh_rotation = np.array([
[1.0, 0.0, 0.0],
[0.0, np.cos(theta), -np.sin(theta)],
[0.0, np.sin(theta), np.cos(theta)],
])
mesh_offset = np.array([0.33, -0.21, 0.0])[:ambient_dim]
for i, resolution in enumerate(builder.resolutions):
from meshmode.mesh.processing import affine_map
from meshmode.discretization.connection import FACE_RESTR_ALL
mesh = builder.get_mesh(resolution, builder.mesh_order)
mesh = affine_map(mesh, A=mesh_rotation, b=mesh_offset)
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory
qtag = dof_desc.DISCR_TAG_QUAD
dcoll = DiscretizationCollection(actx,
mesh,
order=builder.order,
discr_tag_to_group_factory={
qtag:
QuadratureSimplexGroupFactory(
2 * builder.order)
})
volume = dcoll.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume.ndofs)
logger.info("nelements: %d", volume.mesh.nelements)
dd = dof_desc.DD_VOLUME
dq = dd.with_discr_tag(qtag)
df = dof_desc.as_dofdesc(FACE_RESTR_ALL)
ambient_dim = dcoll.ambient_dim
# variables
f_num = f(thaw(dcoll.nodes(dd=dd), actx))
f_quad_num = f(thaw(dcoll.nodes(dd=dq), actx))
from grudge.geometry import normal, summed_curvature
kappa = summed_curvature(actx, dcoll, dd=dq)
normal = normal(actx, dcoll, dd=dq)
face_normal = thaw(dcoll.normal(df), actx)
face_f = op.project(dcoll, dd, df, f_num)
# operators
stiff = op.mass(
dcoll,
sum(
op.local_d_dx(dcoll, i, f_num_i)
for i, f_num_i in enumerate(f_num)))
stiff_t = sum(
op.weak_local_d_dx(dcoll, i, f_num_i)
for i, f_num_i in enumerate(f_num))
kterm = op.mass(dcoll, dq, kappa * f_quad_num.dot(normal))
flux = op.face_mass(dcoll, face_f.dot(face_normal))
# sum everything up
op_global = op.nodal_sum(dcoll, dd, stiff - (stiff_t + kterm))
op_local = op.elementwise_sum(dcoll, dd,
stiff - (stiff_t + kterm + flux))
err_global = abs(op_global)
err_local = op.norm(dcoll, op_local, np.inf)
logger.info("errors: global %.5e local %.5e", err_global, err_local)
# compute max element size
from grudge.dt_utils import h_max_from_volume
h_max = h_max_from_volume(dcoll)
eoc_global.add_data_point(h_max, actx.to_numpy(err_global))
eoc_local.add_data_point(h_max, err_local)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(dcoll)
filename = f"surface_divergence_theorem_{mesh_name}_{i:04d}.vtu"
vis.write_vtk_file(filename, [("r", actx.np.log10(op_local))],
overwrite=True)
# }}}
order = min(builder.order, builder.mesh_order) - 0.5
logger.info("\n%s", str(eoc_global))
logger.info("\n%s", str(eoc_local))
assert eoc_global.max_error() < 1.0e-12 \
or eoc_global.order_estimate() > order - 0.5
assert eoc_local.max_error() < 1.0e-12 \
or eoc_local.order_estimate() > order - 0.5
def _eval_error(x):
return op.norm(dcoll, x, np.inf, dd=df)
def main(ctx_factory, dim=2, order=4, use_quad=False, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue)),
force_device_scalars=True,
)
# {{{ parameters
# sphere radius
radius = 1.0
# sphere resolution
resolution = 64 if dim == 2 else 1
# final time
final_time = np.pi
# flux
flux_type = "lf"
# }}}
# {{{ discretization
if dim == 2:
from meshmode.mesh.generation import make_curve_mesh, ellipse
mesh = make_curve_mesh(
lambda t: radius * ellipse(1.0, t),
np.linspace(0.0, 1.0, resolution + 1),
order)
elif dim == 3:
from meshmode.mesh.generation import generate_icosphere
mesh = generate_icosphere(radius, order=4 * order,
uniform_refinement_rounds=resolution)
else:
raise ValueError("unsupported dimension")
discr_tag_to_group_factory = {}
if use_quad:
qtag = dof_desc.DISCR_TAG_QUAD
else:
qtag = None
from meshmode.discretization.poly_element import \
default_simplex_group_factory, \
QuadratureSimplexGroupFactory
discr_tag_to_group_factory[dof_desc.DISCR_TAG_BASE] = \
default_simplex_group_factory(base_dim=dim-1, order=order)
if use_quad:
discr_tag_to_group_factory[qtag] = \
QuadratureSimplexGroupFactory(order=4*order)
from grudge import DiscretizationCollection
dcoll = DiscretizationCollection(
actx, mesh,
discr_tag_to_group_factory=discr_tag_to_group_factory
)
volume_discr = dcoll.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume_discr.ndofs)
logger.info("nelements: %d", volume_discr.mesh.nelements)
# }}}
# {{{ Surface advection operator
# velocity field
x = thaw(dcoll.nodes(), actx)
c = make_obj_array([-x[1], x[0], 0.0])[:dim]
def f_initial_condition(x):
return x[0]
from grudge.models.advection import SurfaceAdvectionOperator
adv_operator = SurfaceAdvectionOperator(
dcoll,
c,
flux_type=flux_type,
quad_tag=qtag
)
u0 = f_initial_condition(x)
def rhs(t, u):
return adv_operator.operator(t, u)
# check velocity is tangential
from grudge.geometry import normal
surf_normal = normal(actx, dcoll, dd=dof_desc.DD_VOLUME)
error = op.norm(dcoll, c.dot(surf_normal), 2)
logger.info("u_dot_n: %.5e", error)
# }}}
# {{{ time stepping
# FIXME: dt estimate is not necessarily valid for surfaces
dt = actx.to_numpy(
0.45 * adv_operator.estimate_rk4_timestep(actx, dcoll, fields=u0))
nsteps = int(final_time // dt) + 1
logger.info("dt: %.5e", dt)
logger.info("nsteps: %d", nsteps)
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u0, rhs)
plot = Plotter(actx, dcoll, order, visualize=visualize)
norm_u = actx.to_numpy(op.norm(dcoll, u0, 2))
step = 0
event = dt_stepper.StateComputed(0.0, 0, 0, u0)
plot(event, "fld-surface-%04d" % 0)
if visualize and dim == 3:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(dcoll)
vis.write_vtk_file(
"fld-surface-velocity.vtu",
[
("u", c),
("n", surf_normal)
],
overwrite=True
)
df = dof_desc.DOFDesc(FACE_RESTR_INTERIOR)
face_discr = dcoll.discr_from_dd(df)
face_normal = thaw(dcoll.normal(dd=df), actx)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, face_discr)
vis.write_vtk_file("fld-surface-face-normals.vtu", [
("n", face_normal)
], overwrite=True)
for event in dt_stepper.run(t_end=final_time, max_steps=nsteps + 1):
if not isinstance(event, dt_stepper.StateComputed):
continue
step += 1
if step % 10 == 0:
norm_u = actx.to_numpy(op.norm(dcoll, event.state_component, 2))
plot(event, "fld-surface-%04d" % step)
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
# NOTE: These are here to ensure the solution is bounded for the
# time interval specified
assert norm_u < 3
def main():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(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 = 0.75 / (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")
print("%d elements" % mesh.nelements)
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory, \
PolynomialWarpAndBlendGroupFactory
dcoll = DiscretizationCollection(
actx,
mesh,
discr_tag_to_group_factory={
DISCR_TAG_BASE: PolynomialWarpAndBlendGroupFactory(order),
DISCR_TAG_QUAD: QuadratureSimplexGroupFactory(3 * order),
})
# bounded above by 1
c = 0.2 + 0.8 * bump(actx, dcoll, center=np.zeros(3), width=0.5)
fields = flat_obj_array(bump(
actx,
dcoll,
), [dcoll.zeros(actx) for i in range(dcoll.dim)])
vis = make_visualizer(dcoll)
def rhs(t, w):
return wave_operator(dcoll, c=c, w=w)
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, op.norm(dcoll, fields[0], p=2))
vis.write_vtk_file("fld-wave-eager-var-velocity-%04d.vtu" % istep,
[
("c", c),
("u", fields[0]),
("v", fields[1:]),
])
t += dt
istep += 1
def test_convergence_maxwell(actx_factory, order):
"""Test whether 3D Maxwell's actually converges"""
actx = actx_factory()
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
dims = 3
ns = [4, 6, 8]
for n in ns:
mesh = mgen.generate_regular_rect_mesh(a=(0.0, ) * dims,
b=(1.0, ) * dims,
nelements_per_axis=(n, ) * dims)
dcoll = DiscretizationCollection(actx, mesh, order=order)
epsilon = 1
mu = 1
from grudge.models.em import get_rectangular_cavity_mode
def analytic_sol(x, t=0):
return get_rectangular_cavity_mode(actx, x, t, 1, (1, 2, 2))
nodes = thaw(dcoll.nodes(), actx)
fields = analytic_sol(nodes, t=0)
from grudge.models.em import MaxwellOperator
maxwell_operator = MaxwellOperator(dcoll,
epsilon,
mu,
flux_type=0.5,
dimensions=dims)
maxwell_operator.check_bc_coverage(mesh)
def rhs(t, w):
return maxwell_operator.operator(t, w)
dt = maxwell_operator.estimate_rk4_timestep(actx, dcoll)
final_t = dt * 5
nsteps = int(final_t / dt)
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("w", dt, fields, rhs)
logger.info("dt %.5e nsteps %5d", dt, nsteps)
step = 0
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
esc = event.state_component
step += 1
logger.debug("[%04d] t = %.5e", step, event.t)
sol = analytic_sol(nodes, t=step * dt)
total_error = op.norm(dcoll, esc - sol, 2)
eoc_rec.add_data_point(1.0 / n, actx.to_numpy(total_error))
logger.info(
"\n%s", eoc_rec.pretty_print(abscissa_label="h",
error_label="L2 Error"))
assert eoc_rec.order_estimate() > order
