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_operator_compiler_overwrite(actx_factory):
"""Tests that the same expression in ``eval_code`` and ``discr_code``
does not confuse the OperatorCompiler in grudge/symbolic/compiler.py.
"""
actx = actx_factory()
ambient_dim = 2
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
sym_u = sym.nodes(ambient_dim)
sym_div_u = sum(d(u) for d, u in zip(sym.nabla(ambient_dim), sym_u))
div_u = bind(discr, sym_div_u)(actx)
error = bind(discr, sym.norm(2, sym.var("x")))(actx, x=div_u - discr.dim)
logger.info("error: %.5e", error)
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 local_derivatives(self, w):
"""Template for the spatial derivatives of the relevant components of
:math:`E` and :math:`H`
"""
e, h = self.split_eh(w)
nabla = sym.nabla(self.dimensions)
def e_curl(field):
return self.space_cross_e(nabla, field)
def h_curl(field):
return self.space_cross_h(nabla, field)
# in conservation form: u_t + A u_x = 0
return flat_obj_array((self.current - h_curl(h)), e_curl(e))
def sym_operator(self):
u = sym.var("u")
def flux(pair):
return sym.project(pair.dd, "all_faces")(self.flux(pair))
return (-self.v.dot(
sym.nabla(self.ambient_dim) * u
) + sym.InverseMassOperator()(
sym.FaceMassOperator()(
flux(sym.int_tpair(u)) +
flux(sym.bv_tpair(sym.BTAG_ALL, u, self.inflow_u))
# FIXME: Add back support for inflow/outflow tags
#+ flux(sym.bv_tpair(self.inflow_tag, u, bc_in))
#+ flux(sym.bv_tpair(self.outflow_tag, u, bc_out))
)))
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_2d_gauss_theorem(actx_factory):
"""Verify Gauss's theorem explicitly on a mesh"""
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)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
actx = actx_factory()
discr = DGDiscretizationWithBoundaries(actx, mesh, order=2)
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]))
gauss_err = bind(discr,
sym.integral((
sym.nabla(2) * f(sym.nodes(2))
).sum())
- # noqa: W504
sym.integral(
sym.project("vol", sym.BTAG_ALL)(f(sym.nodes(2)))
.dot(sym.normal(sym.BTAG_ALL, 2)),
dd=sym.BTAG_ALL)
)(actx)
assert abs(gauss_err) < 1e-13
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 sym_operator(self):
d = self.ambient_dim
w = sym.make_sym_array("w", d + 1)
u = w[0]
v = w[1:]
# boundary conditions -------------------------------------------------
# dirichlet BCs -------------------------------------------------------
dir_u = sym.cse(sym.project("vol", self.dirichlet_tag)(u))
dir_v = sym.cse(sym.project("vol", self.dirichlet_tag)(v))
if self.dirichlet_bc_f:
# FIXME
from warnings import warn
warn("Inhomogeneous Dirichlet conditions on the wave equation "
"are still having issues.")
dir_g = sym.Field("dir_bc_u")
dir_bc = flat_obj_array(2 * dir_g - dir_u, dir_v)
else:
dir_bc = flat_obj_array(-dir_u, dir_v)
dir_bc = sym.cse(dir_bc, "dir_bc")
# neumann BCs ---------------------------------------------------------
neu_u = sym.cse(sym.project("vol", self.neumann_tag)(u))
neu_v = sym.cse(sym.project("vol", self.neumann_tag)(v))
neu_bc = sym.cse(flat_obj_array(neu_u, -neu_v), "neu_bc")
# radiation BCs -------------------------------------------------------
rad_normal = sym.normal(self.radiation_tag, d)
rad_u = sym.cse(sym.project("vol", self.radiation_tag)(u))
rad_v = sym.cse(sym.project("vol", self.radiation_tag)(v))
rad_bc = sym.cse(
flat_obj_array(
0.5 * (rad_u - self.sign * np.dot(rad_normal, rad_v)), 0.5 *
rad_normal * (np.dot(rad_normal, rad_v) - self.sign * rad_u)),
"rad_bc")
# entire operator -----------------------------------------------------
nabla = sym.nabla(d)
def flux(pair):
return sym.project(pair.dd, "all_faces")(self.flux(pair))
result = (
-flat_obj_array(-self.c * np.dot(nabla, v), -self.c *
(nabla * u)) + # noqa: W504
sym.InverseMassOperator()(
sym.FaceMassOperator()
(flux(sym.int_tpair(w)) +
flux(sym.bv_tpair(self.dirichlet_tag, w, dir_bc)) +
flux(sym.bv_tpair(self.neumann_tag, w, neu_bc)) +
flux(sym.bv_tpair(self.radiation_tag, w, rad_bc)))))
result[0] += self.source_f
return result
def _bound_d_dx(dcoll, xyz_axis):
return bind(dcoll,
sym.nabla(dcoll.dim)[xyz_axis] * sym.Variable("u"),
local_only=True)
def _bound_grad(dcoll):
return bind(dcoll,
sym.nabla(dcoll.dim) * sym.Variable("u"),
local_only=True)
def _bound_grad(self):
return bind(self, sym.nabla(self.dim) * sym.Variable("u"), local_only=True)
def _bound_d_dx(self, xyz_axis):
return bind(self,
sym.nabla(self.dim)[xyz_axis] * sym.Variable("u"),
local_only=True)
