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 gidx, grp_f in enumerate(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._volume_discr.groups[gidx].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))
from meshmode.dof_array import DOFArray, flat_norm
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 flat_norm(elem_mins - ref_mins, ord=np.inf) < 1.e-15
assert flat_norm(elem_maxs - ref_maxs, ord=np.inf) < 1.e-15
assert flat_norm(elem_sums - ref_sums, ord=np.inf) < 1.e-15
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 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