def test_surface_mass_operator_inverse(actx_factory, name):
actx = actx_factory()
# {{{ cases
if name == "2-1-ellipse":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
elif name == "spheroid":
from mesh_data import SpheroidMeshBuilder
builder = SpheroidMeshBuilder()
else:
raise ValueError("unknown geometry name: %s" % name)
# }}}
# {{{ convergence
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for resolution in builder.resolutions:
mesh = builder.get_mesh(resolution, builder.mesh_order)
discr = DiscretizationCollection(actx, mesh, order=builder.order)
volume_discr = discr.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
dd = dof_desc.DD_VOLUME
sym_f = sym.cos(4.0 * sym.nodes(mesh.ambient_dim, dd)[0])
sym_op = sym.InverseMassOperator(dd, dd)(sym.MassOperator(dd, dd)(
sym.var("f")))
f = bind(discr, sym_f)(actx)
f_inv = bind(discr, sym_op)(actx, f=f)
inv_error = bind(
discr,
sym.norm(2,
sym.var("x") - sym.var("y")) / sym.norm(2, sym.var("y")))(
actx, x=f_inv, y=f)
# }}}
h_max = bind(
discr,
sym.h_max_from_volume(discr.ambient_dim, dim=discr.dim,
dd=dd))(actx)
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_1d_mass_mat_trig(ctx_factory):
"""Check the integral of some trig functions on an interval using the mass
matrix
"""
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-4 * np.pi, ),
b=(9 * np.pi, ),
n=(17, ),
order=1)
discr = DGDiscretizationWithBoundaries(cl_ctx, mesh, order=8)
x = sym.nodes(1)
f = bind(discr, sym.cos(x[0])**2)(queue)
ones = bind(discr, sym.Ones(sym.DD_VOLUME))(queue)
mass_op = bind(discr, sym.MassOperator()(sym.var("f")))
num_integral_1 = np.dot(ones.get(), mass_op(queue, f=f))
num_integral_2 = np.dot(f.get(), mass_op(queue, f=ones))
num_integral_3 = bind(discr, sym.integral(sym.var("f")))(queue, f=f)
true_integral = 13 * np.pi / 2
err_1 = abs(num_integral_1 - true_integral)
err_2 = abs(num_integral_2 - true_integral)
err_3 = abs(num_integral_3 - true_integral)
assert err_1 < 1e-10
assert err_2 < 1e-10
assert err_3 < 1e-10
def norm(p, arg, dd=None):
"""
:arg arg: is assumed to be a vector, i.e. have shape ``(n,)``.
"""
sym = _sym()
if dd is None:
dd = sym.DD_VOLUME
dd = sym.as_dofdesc(dd)
if p == 2:
norm_squared = sym.NodalSum(dd_in=dd)(
sym.FunctionSymbol("fabs")(
arg * sym.MassOperator()(arg)))
if isinstance(norm_squared, np.ndarray):
norm_squared = norm_squared.sum()
return sym.FunctionSymbol("sqrt")(norm_squared)
elif p == np.Inf:
result = sym.NodalMax(dd_in=dd)(sym.FunctionSymbol("fabs")(arg))
from pymbolic.primitives import Max
if isinstance(result, np.ndarray):
from functools import reduce
result = reduce(Max, result)
return result
else:
raise ValueError("unsupported value of p")
def test_incorrect_assignment_aggregation(actx_factory, ambient_dim):
"""Tests that the greedy assignemnt aggregation code works on a non-trivial
expression (on which it didn't work at the time of writing).
"""
actx = actx_factory()
target_order = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * ambient_dim,
b=(0.5, ) * ambient_dim,
n=(8, ) * ambient_dim,
order=1)
discr = DiscretizationCollection(actx, mesh, order=target_order)
# {{{ test with a relative norm
from grudge.dof_desc import DD_VOLUME
dd = DD_VOLUME
sym_x = sym.make_sym_array("y", ambient_dim, dd=dd)
sym_y = sym.make_sym_array("y", ambient_dim, dd=dd)
sym_norm_y = sym.norm(2, sym_y, dd=dd)
sym_norm_d = sym.norm(2, sym_x - sym_y, dd=dd)
sym_op = sym_norm_d / sym_norm_y
logger.info("%s", sym.pretty(sym_op))
# FIXME: this shouldn't raise a RuntimeError
with pytest.raises(RuntimeError):
bind(discr, sym_op)(actx, x=1.0, y=discr.discr_from_dd(dd).nodes())
# }}}
# {{{ test with repeated mass inverses
sym_minv_y = sym.cse(sym.InverseMassOperator()(sym_y), "minv_y")
sym_u = make_obj_array([0.5 * sym.Ones(dd), 0.0, 0.0])[:ambient_dim]
sym_div_u = sum(d(u) for d, u in zip(sym.nabla(ambient_dim), sym_u))
sym_op = sym.MassOperator(dd)(sym_u) \
+ sym.MassOperator(dd)(sym_minv_y * sym_div_u)
logger.info("%s", sym.pretty(sym_op))
# FIXME: this shouldn't raise a RuntimeError either
bind(discr, sym_op)(actx, y=discr.discr_from_dd(dd).nodes())
def integral(arg, dd=None):
sym = _sym()
if dd is None:
dd = sym.DD_VOLUME
dd = sym.as_dofdesc(dd)
return sym.NodalSum(dd)(
arg * sym.cse(
sym.MassOperator(dd_in=dd)(sym.Ones(dd)),
"mass_quad_weights",
sym.cse_scope.DISCRETIZATION))
def test_mass_mat_trig(ctx_factory, ambient_dim, quad_tag):
"""Check the integral of some trig functions on an interval using the mass
matrix.
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
nelements = 17
order = 4
a = -4.0 * np.pi
b = +9.0 * np.pi
true_integral = 13 * np.pi / 2 * (b - a)**(ambient_dim - 1)
from meshmode.discretization.poly_element import QuadratureSimplexGroupFactory
dd_quad = sym.DOFDesc(sym.DTAG_VOLUME_ALL, quad_tag)
if quad_tag is sym.QTAG_NONE:
quad_tag_to_group_factory = {}
else:
quad_tag_to_group_factory = {
quad_tag: QuadratureSimplexGroupFactory(order=2 * order)
}
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(a, ) * ambient_dim,
b=(b, ) * ambient_dim,
n=(nelements, ) * ambient_dim,
order=1)
discr = DGDiscretizationWithBoundaries(
actx,
mesh,
order=order,
quad_tag_to_group_factory=quad_tag_to_group_factory)
def _get_variables_on(dd):
sym_f = sym.var("f", dd=dd)
sym_x = sym.nodes(ambient_dim, dd=dd)
sym_ones = sym.Ones(dd)
return sym_f, sym_x, sym_ones
sym_f, sym_x, sym_ones = _get_variables_on(sym.DD_VOLUME)
f_volm = actx.to_numpy(flatten(bind(discr, sym.cos(sym_x[0])**2)(actx)))
ones_volm = actx.to_numpy(flatten(bind(discr, sym_ones)(actx)))
sym_f, sym_x, sym_ones = _get_variables_on(dd_quad)
f_quad = bind(discr, sym.cos(sym_x[0])**2)(actx)
ones_quad = bind(discr, sym_ones)(actx)
mass_op = bind(discr, sym.MassOperator(dd_quad, sym.DD_VOLUME)(sym_f))
num_integral_1 = np.dot(ones_volm,
actx.to_numpy(flatten(mass_op(f=f_quad))))
err_1 = abs(num_integral_1 - true_integral)
assert err_1 < 1e-9, err_1
num_integral_2 = np.dot(f_volm,
actx.to_numpy(flatten(mass_op(f=ones_quad))))
err_2 = abs(num_integral_2 - true_integral)
assert err_2 < 1.0e-9, err_2
if quad_tag is sym.QTAG_NONE:
# NOTE: `integral` always makes a square mass matrix and
# `QuadratureSimplexGroupFactory` does not have a `mass_matrix` method.
num_integral_3 = bind(discr, sym.integral(sym_f, dd=dd_quad))(f=f_quad)
err_3 = abs(num_integral_3 - true_integral)
assert err_3 < 5.0e-10, err_3
def test_mass_mat_trig(actx_factory, ambient_dim, discr_tag):
"""Check the integral of some trig functions on an interval using the mass
matrix.
"""
actx = actx_factory()
nel_1d = 16
order = 4
a = -4.0 * np.pi
b = +9.0 * np.pi
true_integral = 13 * np.pi / 2 * (b - a)**(ambient_dim - 1)
from meshmode.discretization.poly_element import QuadratureSimplexGroupFactory
dd_quad = dof_desc.DOFDesc(dof_desc.DTAG_VOLUME_ALL, discr_tag)
if discr_tag is dof_desc.DISCR_TAG_BASE:
discr_tag_to_group_factory = {}
else:
discr_tag_to_group_factory = {
discr_tag: QuadratureSimplexGroupFactory(order=2 * order)
}
mesh = mgen.generate_regular_rect_mesh(a=(a, ) * ambient_dim,
b=(b, ) * ambient_dim,
nelements_per_axis=(nel_1d, ) *
ambient_dim,
order=1)
discr = DiscretizationCollection(
actx,
mesh,
order=order,
discr_tag_to_group_factory=discr_tag_to_group_factory)
def _get_variables_on(dd):
sym_f = sym.var("f", dd=dd)
sym_x = sym.nodes(ambient_dim, dd=dd)
sym_ones = sym.Ones(dd)
return sym_f, sym_x, sym_ones
sym_f, sym_x, sym_ones = _get_variables_on(dof_desc.DD_VOLUME)
f_volm = actx.to_numpy(flatten(bind(discr, sym.cos(sym_x[0])**2)(actx)))
ones_volm = actx.to_numpy(flatten(bind(discr, sym_ones)(actx)))
sym_f, sym_x, sym_ones = _get_variables_on(dd_quad)
f_quad = bind(discr, sym.cos(sym_x[0])**2)(actx)
ones_quad = bind(discr, sym_ones)(actx)
mass_op = bind(discr, sym.MassOperator(dd_quad, dof_desc.DD_VOLUME)(sym_f))
num_integral_1 = np.dot(ones_volm,
actx.to_numpy(flatten(mass_op(f=f_quad))))
err_1 = abs(num_integral_1 - true_integral)
assert err_1 < 2e-9, err_1
num_integral_2 = np.dot(f_volm,
actx.to_numpy(flatten(mass_op(f=ones_quad))))
err_2 = abs(num_integral_2 - true_integral)
assert err_2 < 2e-9, err_2
if discr_tag is dof_desc.DISCR_TAG_BASE:
# NOTE: `integral` always makes a square mass matrix and
# `QuadratureSimplexGroupFactory` does not have a `mass_matrix` method.
num_integral_3 = bind(discr, sym.integral(sym_f, dd=dd_quad))(f=f_quad)
err_3 = abs(num_integral_3 - true_integral)
assert err_3 < 5.0e-10, err_3
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)
# }}}
# {{{ convergene
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]
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
discr = DiscretizationCollection(actx,
mesh,
order=builder.order,
discr_tag_to_group_factory={
"product":
QuadratureSimplexGroupFactory(
2 * builder.order)
})
volume = discr.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("product")
df = dof_desc.as_dofdesc(FACE_RESTR_ALL)
ambient_dim = discr.ambient_dim
dim = discr.dim
# variables
sym_f = f(sym.nodes(ambient_dim, dd=dd))
sym_f_quad = f(sym.nodes(ambient_dim, dd=dq))
sym_kappa = sym.summed_curvature(ambient_dim, dim=dim, dd=dq)
sym_normal = sym.surface_normal(ambient_dim, dim=dim,
dd=dq).as_vector()
sym_face_normal = sym.normal(df, ambient_dim, dim=dim - 1)
sym_face_f = sym.project(dd, df)(sym_f)
# operators
sym_stiff = sum(
sym.StiffnessOperator(d)(f) for d, f in enumerate(sym_f))
sym_stiff_t = sum(
sym.StiffnessTOperator(d)(f) for d, f in enumerate(sym_f))
sym_k = sym.MassOperator(dq,
dd)(sym_kappa * sym_f_quad.dot(sym_normal))
sym_flux = sym.FaceMassOperator()(sym_face_f.dot(sym_face_normal))
# sum everything up
sym_op_global = sym.NodalSum(dd)(sym_stiff - (sym_stiff_t + sym_k))
sym_op_local = sym.ElementwiseSumOperator(dd)(sym_stiff -
(sym_stiff_t + sym_k +
sym_flux))
# evaluate
op_global = bind(discr, sym_op_global)(actx)
op_local = bind(discr, sym_op_local)(actx)
err_global = abs(op_global)
err_local = bind(discr, sym.norm(np.inf, sym.var("x")))(actx,
x=op_local)
logger.info("errors: global %.5e local %.5e", err_global, err_local)
# compute max element size
h_max = bind(
discr,
sym.h_max_from_volume(discr.ambient_dim, dim=discr.dim,
dd=dd))(actx)
eoc_global.add_data_point(h_max, err_global)
eoc_local.add_data_point(h_max, err_local)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=builder.order)
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_mass_surface_area(actx_factory, name):
actx = actx_factory()
# {{{ cases
if name == "2-1-ellipse":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
surface_area = _ellipse_surface_area(builder.radius,
builder.aspect_ratio)
elif name == "spheroid":
from mesh_data import SpheroidMeshBuilder
builder = SpheroidMeshBuilder()
surface_area = _spheroid_surface_area(builder.radius,
builder.aspect_ratio)
elif name == "box2d":
from mesh_data import BoxMeshBuilder
builder = BoxMeshBuilder(ambient_dim=2)
surface_area = 1.0
elif name == "box3d":
from mesh_data import BoxMeshBuilder
builder = BoxMeshBuilder(ambient_dim=3)
surface_area = 1.0
else:
raise ValueError("unknown geometry name: %s" % name)
# }}}
# {{{ convergence
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for resolution in builder.resolutions:
mesh = builder.get_mesh(resolution, builder.mesh_order)
discr = DiscretizationCollection(actx, mesh, order=builder.order)
volume_discr = discr.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume_discr.ndofs)
logger.info("nelements: %d", volume_discr.mesh.nelements)
# {{{ compute surface area
dd = dof_desc.DD_VOLUME
sym_op = sym.NodalSum(dd)(sym.MassOperator(dd, dd)(sym.Ones(dd)))
approx_surface_area = bind(discr, sym_op)(actx)
logger.info("surface: got {:.5e} / expected {:.5e}".format(
approx_surface_area, surface_area))
area_error = abs(approx_surface_area -
surface_area) / abs(surface_area)
# }}}
h_max = bind(
discr,
sym.h_max_from_volume(discr.ambient_dim, dim=discr.dim,
dd=dd))(actx)
eoc.add_data_point(h_max, area_error + 1.0e-16)
# }}}
logger.info("surface area error\n%s", str(eoc))
assert eoc.max_error() < 1.0e-14 \
or eoc.order_estimate() > builder.order
def _bound_mass(dcoll, dd):
return bind(dcoll,
sym.MassOperator(dd_in=dd)(sym.Variable("u", dd)),
local_only=True)
