def test_circle_mesh(visualize=False):
from meshmode.mesh.io import generate_gmsh, FileSource
logger.info("BEGIN GEN")
mesh = generate_gmsh(
FileSource("circle.step"),
2,
order=2,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.05;"],
target_unit="MM",
)
logger.info("END GEN")
logger.info("nelements: %d", mesh.nelements)
from meshmode.mesh.processing import affine_map
mesh = affine_map(mesh, A=3 * np.eye(2))
if visualize:
from meshmode.mesh.visualization import draw_2d_mesh
draw_2d_mesh(mesh,
fill=None,
draw_vertex_numbers=False,
draw_nodal_adjacency=True,
set_bounding_box=True)
import matplotlib.pyplot as pt
pt.axis("equal")
pt.savefig("circle_mesh", dpi=300)
def test_merge_and_map(ctx_getter, visualize=False):
from meshmode.mesh.io import generate_gmsh, FileSource
mesh_order = 3
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"]
)
from meshmode.mesh.processing import merge_dijsoint_meshes, affine_map
mesh2 = affine_map(mesh, A=np.eye(2), b=np.array([5, 0]))
mesh3 = merge_dijsoint_meshes((mesh2, mesh))
if visualize:
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
discr = Discretization(cl_ctx, mesh3,
PolynomialWarpAndBlendGroupFactory(3))
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(queue, discr, 1)
vis.write_vtk_file("merged.vtu", [])
def get_mesh(self, resolution, mesh_order):
from meshmode.mesh.io import generate_gmsh, FileSource
base_mesh = generate_gmsh(FileSource("ellipsoid.step"),
2,
order=mesh_order,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" %
resolution
])
from meshmode.mesh.processing import perform_flips
base_mesh = perform_flips(base_mesh, np.ones(base_mesh.nelements))
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
from meshmode.mesh.tools import rand_rotation_matrix
meshes = [
affine_map(base_mesh,
A=rand_rotation_matrix(3),
b=self.pitch * np.array([(ix - self.nx // 2),
(iy - self.ny // 2),
(iz - self.ny // 2)]))
for ix in range(self.nx) for iy in range(self.ny)
for iz in range(self.nz)
]
return merge_disjoint_meshes(meshes, single_group=True)
def get_mesh(self, resolution, target_order):
from meshmode.mesh.io import generate_gmsh, FileSource
base_mesh = generate_gmsh(
FileSource("ellipsoid.step"), 2, order=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
base_mesh = perform_flips(base_mesh, np.ones(base_mesh.nelements))
from meshmode.mesh.processing import affine_map, merge_disjoint_meshes
from meshmode.mesh.tools import rand_rotation_matrix
pitch = 10
meshes = [
affine_map(
base_mesh,
A=rand_rotation_matrix(3),
b=pitch*np.array([
(ix-self.nx//2),
(iy-self.ny//2),
(iz-self.ny//2)]))
for ix in range(self.nx)
for iy in range(self.ny)
for iz in range(self.nz)
]
mesh = merge_disjoint_meshes(meshes, single_group=True)
return mesh
def test_element_orientation():
from meshmode.mesh.io import generate_gmsh, FileSource
mesh_order = 3
mesh = generate_gmsh(
FileSource("blob-2d.step"),
2,
order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"])
from meshmode.mesh.processing import (perform_flips,
find_volume_mesh_element_orientations
)
mesh_orient = find_volume_mesh_element_orientations(mesh)
assert (mesh_orient > 0).all()
from random import randrange
flippy = np.zeros(mesh.nelements, np.int8)
for i in range(int(0.3 * mesh.nelements)):
flippy[randrange(0, mesh.nelements)] = 1
mesh = perform_flips(mesh, flippy, skip_tests=True)
mesh_orient = find_volume_mesh_element_orientations(mesh)
assert ((mesh_orient < 0) == (flippy > 0)).all()
def test_element_orientation():
from meshmode.mesh.io import generate_gmsh, FileSource
mesh_order = 3
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"]
)
from meshmode.mesh.processing import (perform_flips,
find_volume_mesh_element_orientations)
mesh_orient = find_volume_mesh_element_orientations(mesh)
assert (mesh_orient > 0).all()
from random import randrange
flippy = np.zeros(mesh.nelements, np.int8)
for i in range(int(0.3*mesh.nelements)):
flippy[randrange(0, mesh.nelements)] = 1
mesh = perform_flips(mesh, flippy, skip_tests=True)
mesh_orient = find_volume_mesh_element_orientations(mesh)
assert ((mesh_orient < 0) == (flippy > 0)).all()
def gen_blob_mesh(h=0.2, order=1):
from meshmode.mesh.io import generate_gmsh, FileSource
return generate_gmsh(
FileSource("blob-2d.step"),
2,
order=order,
force_ambient_dim=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %s;" % h])
def get_mesh(self, resolution, target_order):
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("ellipsoid.step"), 2, order=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
return perform_flips(mesh, np.ones(mesh.nelements))
def test_quad_mesh_3d(mesh_name, order=3, visualize=False):
if mesh_name == "ball":
from meshmode.mesh.io import ScriptWithFilesSource
script = ScriptWithFilesSource(
"""
Merge "ball-radius-1.step";
// Mesh.CharacteristicLengthMax = 0.1;
Mesh.RecombineAll = 1;
Mesh.Recombine3DAll = 1;
Mesh.Recombine3DLevel = 2;
Mesh.Algorithm = 8;
Mesh.Algorithm3D = 8;
Mesh 3;
Save "output.msh";
""", ["ball-radius-1.step"])
with open("ball-quad.geo", "w") as f:
f.write(script.source)
elif mesh_name == "cube":
from meshmode.mesh.io import ScriptSource
script = ScriptSource(
"""
SetFactory("OpenCASCADE");
Box(1) = {0, 0, 0, 1, 1, 1};
Transfinite Line "*" = 8;
Transfinite Surface "*";
Transfinite Volume "*";
Mesh.RecombineAll = 1;
Mesh.Recombine3DAll = 1;
Mesh.Recombine3DLevel = 2;
""", "geo")
else:
raise ValueError(f"unknown mesh name: '{mesh_name}'")
np.set_printoptions(linewidth=200)
from meshmode.mesh.io import generate_gmsh
logger.info("BEGIN GEN")
mesh = generate_gmsh(script, 3, order=order, target_unit="MM")
logger.info("END GEN")
if visualize:
from meshmode.mesh.visualization import write_vertex_vtk_file
write_vertex_vtk_file(mesh,
f"quad_mesh_3d_{mesh_name}.vtu",
overwrite=True)
def test_merge_and_map(ctx_factory, visualize=False):
from meshmode.mesh.io import generate_gmsh, FileSource
from meshmode.mesh.generation import generate_box_mesh
from meshmode.mesh import TensorProductElementGroup
from meshmode.discretization.poly_element import (
PolynomialWarpAndBlendGroupFactory,
LegendreGaussLobattoTensorProductGroupFactory)
mesh_order = 3
if 1:
mesh = generate_gmsh(
FileSource("blob-2d.step"),
2,
order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"])
discr_grp_factory = PolynomialWarpAndBlendGroupFactory(3)
else:
mesh = generate_box_mesh((
np.linspace(0, 1, 4),
np.linspace(0, 1, 4),
np.linspace(0, 1, 4),
),
10,
group_factory=TensorProductElementGroup)
discr_grp_factory = LegendreGaussLobattoTensorProductGroupFactory(3)
from meshmode.mesh.processing import merge_disjoint_meshes, affine_map
mesh2 = affine_map(mesh,
A=np.eye(mesh.ambient_dim),
b=np.array([5, 0, 0])[:mesh.ambient_dim])
mesh3 = merge_disjoint_meshes((mesh2, mesh))
mesh3.facial_adjacency_groups
mesh3.copy()
if visualize:
from meshmode.discretization import Discretization
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
discr = Discretization(cl_ctx, mesh3, discr_grp_factory)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(queue, discr, 3, element_shrink_factor=0.8)
vis.write_vtk_file("merged.vtu", [])
def get_mesh(self, resolution, target_order):
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(FileSource("ellipsoid.step"),
2,
order=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" %
resolution
])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
return perform_flips(mesh, np.ones(mesh.nelements))
def test_merge_and_map(ctx_factory, visualize=False):
from meshmode.mesh.io import generate_gmsh, FileSource
from meshmode.mesh.generation import generate_box_mesh
from meshmode.mesh import TensorProductElementGroup
from meshmode.discretization.poly_element import (
PolynomialWarpAndBlendGroupFactory,
LegendreGaussLobattoTensorProductGroupFactory)
mesh_order = 3
if 1:
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"]
)
discr_grp_factory = PolynomialWarpAndBlendGroupFactory(3)
else:
mesh = generate_box_mesh(
(
np.linspace(0, 1, 4),
np.linspace(0, 1, 4),
np.linspace(0, 1, 4),
),
10, group_factory=TensorProductElementGroup)
discr_grp_factory = LegendreGaussLobattoTensorProductGroupFactory(3)
from meshmode.mesh.processing import merge_disjoint_meshes, affine_map
mesh2 = affine_map(mesh,
A=np.eye(mesh.ambient_dim),
b=np.array([5, 0, 0])[:mesh.ambient_dim])
mesh3 = merge_disjoint_meshes((mesh2, mesh))
mesh3.facial_adjacency_groups
mesh3.copy()
if visualize:
from meshmode.discretization import Discretization
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
discr = Discretization(cl_ctx, mesh3, discr_grp_factory)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(queue, discr, 3, element_shrink_factor=0.8)
vis.write_vtk_file("merged.vtu", [])
def test_mesh_to_tikz():
from meshmode.mesh.io import generate_gmsh, FileSource
h = 0.3
order = 1
mesh = generate_gmsh(
FileSource("../test/blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
from meshmode.mesh.visualization import mesh_to_tikz
mesh_to_tikz(mesh)
def get_mesh(self, resolution, target_order):
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("rounded-cube.step"), 2, order=3,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
from meshmode.mesh.processing import perform_flips, affine_map
mesh = affine_map(mesh, b=np.array([-0.5, -0.5, -0.5]))
mesh = affine_map(mesh, A=np.eye(3)*2)
# now centered at origin and extends to -1,1
# Flip elements--gmsh generates inside-out geometry.
return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order):
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("rounded-cube.step"), 2, order=3,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
from meshmode.mesh.processing import perform_flips, affine_map
mesh = affine_map(mesh, b=np.array([-0.5, -0.5, -0.5]))
mesh = affine_map(mesh, A=np.eye(3)*2)
# now centered at origin and extends to -1,1
# Flip elements--gmsh generates inside-out geometry.
return perform_flips(mesh, np.ones(mesh.nelements))
def test_quad_mesh_2d():
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
print("BEGIN GEN")
mesh = generate_gmsh(
ScriptWithFilesSource(
"""
Merge "blob-2d.step";
Mesh.CharacteristicLengthMax = 0.05;
Recombine Surface "*" = 0.0001;
Mesh 2;
Save "output.msh";
""", ["blob-2d.step"]),
force_ambient_dim=2,
)
print("END GEN")
print(mesh.nelements)
def test_merge_and_map(actx_factory, group_cls, visualize=False):
from meshmode.mesh.io import generate_gmsh, FileSource
order = 3
mesh_order = 3
if group_cls is SimplexElementGroup:
mesh = generate_gmsh(
FileSource("blob-2d.step"),
2,
order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = 0.02;"],
target_unit="MM",
)
discr_grp_factory = PolynomialWarpAndBlendGroupFactory(order)
else:
ambient_dim = 3
mesh = mgen.generate_regular_rect_mesh(a=(0, ) * ambient_dim,
b=(1, ) * ambient_dim,
nelements_per_axis=(4, ) *
ambient_dim,
order=mesh_order,
group_cls=group_cls)
discr_grp_factory = LegendreGaussLobattoTensorProductGroupFactory(
order)
from meshmode.mesh.processing import merge_disjoint_meshes, affine_map
mesh2 = affine_map(mesh,
A=np.eye(mesh.ambient_dim),
b=np.array([2, 0, 0])[:mesh.ambient_dim])
mesh3 = merge_disjoint_meshes((mesh2, mesh))
assert mesh3.facial_adjacency_groups
mesh4 = mesh3.copy()
if visualize:
from meshmode.discretization import Discretization
actx = actx_factory()
discr = Discretization(actx, mesh4, discr_grp_factory)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, discr, 3, element_shrink_factor=0.8)
vis.write_vtk_file("merge_and_map.vtu", [])
def test_quad_mesh():
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
print("BEGIN GEN")
mesh = generate_gmsh(
ScriptWithFilesSource(
"""
Merge "blob-2d.step";
Mesh.CharacteristicLengthMax = 0.05;
Recombine Surface "*" = 0.0001;
Mesh 2;
Save "output.msh";
""",
["blob-2d.step"]),
force_ambient_dim=2,
)
print("END GEN")
print(mesh.nelements)
def test_boundary_interpolation(ctx_getter):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.mesh.io import generate_gmsh, FileSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
from meshmode.discretization.connection import make_boundary_restriction
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
for h in [1e-1, 3e-2, 1e-2]:
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
print("END GEN")
vol_discr = Discretization(cl_ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(order))
print("h=%s -> %d elements" % (
h, sum(mgrp.nelements for mgrp in mesh.groups)))
x = vol_discr.nodes()[0].with_queue(queue)
f = 0.1*cl.clmath.sin(30*x)
bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction(
queue, vol_discr, InterpolatoryQuadratureSimplexGroupFactory(order))
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = 0.1*cl.clmath.sin(30*bdry_x)
bdry_f_2 = bdry_connection(queue, f)
err = la.norm((bdry_f-bdry_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert eoc_rec.order_estimate() >= order-0.5
def test_quad_mesh_2d(ambient_dim, filename, visualize=False):
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
logger.info("BEGIN GEN")
mesh = generate_gmsh(
ScriptWithFilesSource(
f"""
Merge "{filename}";
Mesh.CharacteristicLengthMax = 0.05;
Recombine Surface "*" = 0.0001;
Mesh 2;
Save "output.msh";
""", [filename]),
order=1,
force_ambient_dim=ambient_dim,
target_unit="MM",
)
logger.info("END GEN")
logger.info("nelements: %d", mesh.nelements)
groups = []
for grp in mesh.groups:
if not isinstance(grp, TensorProductElementGroup):
# NOTE: gmsh isn't guaranteed to recombine all elements, so we
# could still have some simplices sitting around, so skip them
groups.append(grp.copy())
continue
g = mgen.make_group_from_vertices(mesh.vertices,
grp.vertex_indices,
grp.order,
group_cls=TensorProductElementGroup)
assert g.nodes.shape == (mesh.ambient_dim, grp.nelements,
grp.nunit_nodes)
groups.append(g)
mesh_from_vertices = Mesh(mesh.vertices, groups=groups, is_conforming=True)
if visualize:
from meshmode.mesh.visualization import write_vertex_vtk_file
write_vertex_vtk_file(mesh, "quad_mesh_2d_orig.vtu")
write_vertex_vtk_file(mesh_from_vertices, "quad_mesh_2d_groups.vtu")
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/master/"
"surface-3d/elliptiplane.brep")
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("elliptiplane.brep"), 2, order=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
# now centered at origin and extends to -1,1
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/master/"
"surface-3d/elliptiplane.brep")
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("elliptiplane.brep"), 2, order=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
# now centered at origin and extends to -1,1
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
def test_circle_mesh(do_plot=False):
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("circle.step"), 2, order=2,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = 0.05;"]
)
print("END GEN")
print(mesh.nelements)
from meshmode.mesh.processing import affine_map
mesh = affine_map(mesh, A=3*np.eye(2))
if do_plot:
from meshmode.mesh.visualization import draw_2d_mesh
draw_2d_mesh(mesh, fill=None, draw_nodal_adjacency=True,
set_bounding_box=True)
import matplotlib.pyplot as pt
pt.show()
def test_circle_mesh(do_plot=False):
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("circle.step"), 2, order=2,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = 0.05;"]
)
print("END GEN")
print(mesh.nelements)
from meshmode.mesh.processing import affine_map
mesh = affine_map(mesh, A=3*np.eye(2))
if do_plot:
from meshmode.mesh.visualization import draw_2d_mesh
draw_2d_mesh(mesh, fill=None, draw_connectivity=True,
set_bounding_box=True)
import matplotlib.pyplot as pt
pt.show()
def test_interpolatory_error_reporting(ctx_factory):
logging.basicConfig(level=logging.INFO)
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
h = 0.2
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("circle.step"),
2,
order=4,
force_ambient_dim=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %g;" % h],
target_unit="mm",
)
logger.info("%d elements" % mesh.nelements)
# {{{ discretizations and connections
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory
vol_discr = Discretization(ctx, mesh, QuadratureSimplexGroupFactory(5))
vol_x = vol_discr.nodes().with_queue(queue)
# }}}
from pytential import integral
rhs = 1 + 0 * vol_x[0]
one = rhs.copy()
one.fill(1)
with pytest.raises(TypeError):
print("AREA", integral(vol_discr, queue, one), 0.25**2 * np.pi)
def test_interpolatory_error_reporting(ctx_factory):
logging.basicConfig(level=logging.INFO)
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
h = 0.2
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("circle.step"),
2,
order=4,
force_ambient_dim=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %g;" % h],
target_unit="mm",
)
logger.info("%d elements" % mesh.nelements)
# {{{ discretizations and connections
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory
vol_discr = Discretization(actx, mesh, QuadratureSimplexGroupFactory(5))
from meshmode.dof_array import thaw
vol_x = thaw(actx, vol_discr.nodes())
# }}}
from pytential import integral
one = 1 + 0 * vol_x[0]
from meshmode.discretization import NoninterpolatoryElementGroupError
with pytest.raises(NoninterpolatoryElementGroupError):
print("AREA", integral(vol_discr, one), 0.25**2 * np.pi)
def no_test_quad_mesh_3d():
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
print("BEGIN GEN")
mesh = generate_gmsh(
ScriptWithFilesSource(
"""
Merge "ball-radius-1.step";
// Mesh.CharacteristicLengthMax = 0.1;
Mesh.RecombineAll=1;
Mesh.Recombine3DAll=1;
Mesh.Algorithm = 8;
Mesh.Algorithm3D = 9;
// Mesh.Smoothing = 0;
// Mesh.ElementOrder = 3;
Mesh 3;
Save "output.msh";
""", ["ball-radius-1.step"]), )
print("END GEN")
print(mesh.nelements)
def get_mesh(self, resolution, mesh_order):
from meshmode.mesh.io import ScriptSource
source = ScriptSource(
"""
SetFactory("OpenCASCADE");
Sphere(1) = {{0, 0, 0, {r}}};
Dilate {{ {{0, 0, 0}}, {{ {r}, {r}, {rr} }} }} {{ Volume{{1}}; }}
""".format(r=self.diameter, rr=self.aspect_ratio * self.diameter),
"geo")
from meshmode.mesh.io import generate_gmsh
mesh = generate_gmsh(source,
2,
order=mesh_order,
other_options=[
"-optimize_ho", "-string",
"Mesh.CharacteristicLengthMax = %g;" %
resolution
],
target_unit="MM")
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
def no_test_quad_mesh_3d():
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
print("BEGIN GEN")
mesh = generate_gmsh(
ScriptWithFilesSource(
"""
Merge "ball-radius-1.step";
// Mesh.CharacteristicLengthMax = 0.1;
Mesh.RecombineAll=1;
Mesh.Recombine3DAll=1;
Mesh.Algorithm = 8;
Mesh.Algorithm3D = 9;
// Mesh.Smoothing = 0;
// Mesh.ElementOrder = 3;
Mesh 3;
Save "output.msh";
""",
["ball-radius-1.step"]),
)
print("END GEN")
print(mesh.nelements)
def test_opposite_face_interpolation(ctx_getter, group_factory,
mesh_name, dim, mesh_pars):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, make_opposite_face_connection,
check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 5
def f(x):
return 0.1*cl.clmath.sin(30*x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
print("END GEN")
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1/mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(cl_ctx, mesh,
group_factory(order))
print("h=%s -> %d elements" % (
h, sum(mgrp.nelements for mgrp in mesh.groups)))
bdry_connection = make_face_restriction(
vol_discr, group_factory(order),
FRESTR_INTERIOR_FACES)
bdry_discr = bdry_connection.to_discr
opp_face = make_opposite_face_connection(bdry_connection)
check_connection(opp_face)
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
bdry_f_2 = opp_face(queue, bdry_f)
err = la.norm((bdry_f-bdry_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (
eoc_rec.order_estimate() >= order-0.5
or eoc_rec.max_error() < 1e-13)
def test_sanity_balls(ctx_getter, src_file, dim, mesh_order, visualize=False):
pytest.importorskip("pytential")
logging.basicConfig(level=logging.INFO)
ctx = ctx_getter()
queue = cl.CommandQueue(ctx)
from pytools.convergence import EOCRecorder
vol_eoc_rec = EOCRecorder()
surf_eoc_rec = EOCRecorder()
# overkill
quad_order = mesh_order
from pytential import bind, sym
for h in [0.2, 0.14, 0.1]:
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(FileSource(src_file),
dim,
order=mesh_order,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % h
],
force_ambient_dim=dim)
logger.info("%d elements" % mesh.nelements)
# {{{ discretizations and connections
from meshmode.discretization import Discretization
vol_discr = Discretization(
ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(quad_order))
from meshmode.discretization.connection import make_face_restriction
bdry_connection = make_face_restriction(
vol_discr, InterpolatoryQuadratureSimplexGroupFactory(quad_order),
BTAG_ALL)
bdry_discr = bdry_connection.to_discr
# }}}
# {{{ visualizers
from meshmode.discretization.visualization import make_visualizer
vol_vis = make_visualizer(queue, vol_discr, 20)
bdry_vis = make_visualizer(queue, bdry_discr, 20)
# }}}
from math import gamma
true_surf = 2 * np.pi**(dim / 2) / gamma(dim / 2)
true_vol = true_surf / dim
vol_x = vol_discr.nodes().with_queue(queue)
vol_one = vol_x[0].copy()
vol_one.fill(1)
from pytential import norm, integral # noqa
comp_vol = integral(vol_discr, queue, vol_one)
rel_vol_err = abs(true_vol - comp_vol) / true_vol
vol_eoc_rec.add_data_point(h, rel_vol_err)
print("VOL", true_vol, comp_vol)
bdry_x = bdry_discr.nodes().with_queue(queue)
bdry_one_exact = bdry_x[0].copy()
bdry_one_exact.fill(1)
bdry_one = bdry_connection(queue, vol_one).with_queue(queue)
intp_err = norm(bdry_discr, queue, bdry_one - bdry_one_exact)
assert intp_err < 1e-14
comp_surf = integral(bdry_discr, queue, bdry_one)
rel_surf_err = abs(true_surf - comp_surf) / true_surf
surf_eoc_rec.add_data_point(h, rel_surf_err)
print("SURF", true_surf, comp_surf)
if visualize:
vol_vis.write_vtk_file("volume-h=%g.vtu" % h, [
("f", vol_one),
("area_el", bind(vol_discr, sym.area_element())(queue)),
])
bdry_vis.write_vtk_file("boundary-h=%g.vtu" % h, [("f", bdry_one)])
# {{{ check normals point outward
normal_outward_check = bind(
bdry_discr,
sym.normal(mesh.ambient_dim) | sym.nodes(mesh.ambient_dim),
)(queue).as_scalar() > 0
assert normal_outward_check.get().all(), normal_outward_check.get()
# }}}
print("---------------------------------")
print("VOLUME")
print("---------------------------------")
print(vol_eoc_rec)
assert vol_eoc_rec.order_estimate() >= mesh_order
print("---------------------------------")
print("SURFACE")
print("---------------------------------")
print(surf_eoc_rec)
assert surf_eoc_rec.order_estimate() >= mesh_order
def test_opposite_face_interpolation(ctx_getter, group_factory, mesh_name, dim,
mesh_pars):
logging.basicConfig(level=logging.INFO)
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, make_opposite_face_connection, check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 5
def f(x):
return 0.1 * cl.clmath.sin(30 * x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(FileSource("blob-2d.step"),
2,
order=order,
force_ambient_dim=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %s;" % h
])
print("END GEN")
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(cl_ctx, mesh, group_factory(order))
print("h=%s -> %d elements" %
(h, sum(mgrp.nelements for mgrp in mesh.groups)))
bdry_connection = make_face_restriction(vol_discr,
group_factory(order),
FRESTR_INTERIOR_FACES)
bdry_discr = bdry_connection.to_discr
opp_face = make_opposite_face_connection(bdry_connection)
check_connection(opp_face)
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
bdry_f_2 = opp_face(queue, bdry_f)
err = la.norm((bdry_f - bdry_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-13)
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/a869fc3/"
"surface-3d/betterplane.brep")
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
mesh = generate_gmsh(
ScriptWithFilesSource(
"""
Merge "betterplane.brep";
Mesh.CharacteristicLengthMax = %(lcmax)f;
Mesh.ElementOrder = 2;
Mesh.CharacteristicLengthExtendFromBoundary = 0;
// 2D mesh optimization
// Mesh.Lloyd = 1;
l_superfine() = Unique(Abs(Boundary{ Surface{
27, 25, 17, 13, 18 }; }));
l_fine() = Unique(Abs(Boundary{ Surface{ 2, 6, 7}; }));
l_coarse() = Unique(Abs(Boundary{ Surface{ 14, 16 }; }));
// p() = Unique(Abs(Boundary{ Line{l_fine()}; }));
// Characteristic Length{p()} = 0.05;
Field[1] = Attractor;
Field[1].NNodesByEdge = 100;
Field[1].EdgesList = {l_superfine()};
Field[2] = Threshold;
Field[2].IField = 1;
Field[2].LcMin = 0.075;
Field[2].LcMax = %(lcmax)f;
Field[2].DistMin = 0.1;
Field[2].DistMax = 0.4;
Field[3] = Attractor;
Field[3].NNodesByEdge = 100;
Field[3].EdgesList = {l_fine()};
Field[4] = Threshold;
Field[4].IField = 3;
Field[4].LcMin = 0.1;
Field[4].LcMax = %(lcmax)f;
Field[4].DistMin = 0.15;
Field[4].DistMax = 0.4;
Field[5] = Attractor;
Field[5].NNodesByEdge = 100;
Field[5].EdgesList = {l_coarse()};
Field[6] = Threshold;
Field[6].IField = 5;
Field[6].LcMin = 0.15;
Field[6].LcMax = %(lcmax)f;
Field[6].DistMin = 0.2;
Field[6].DistMax = 0.4;
Field[7] = Min;
Field[7].FieldsList = {2, 4, 6};
Background Field = 7;
""" % {
"lcmax": resolution,
}, ["betterplane.brep"]), 2)
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
def test_sanity_balls(actx_factory,
src_file,
dim,
mesh_order,
visualize=False):
pytest.importorskip("pytential")
logging.basicConfig(level=logging.INFO)
actx = actx_factory()
from pytools.convergence import EOCRecorder
vol_eoc_rec = EOCRecorder()
surf_eoc_rec = EOCRecorder()
# overkill
quad_order = mesh_order
from pytential import bind, sym
for h in [0.2, 0.1, 0.05]:
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(FileSource(src_file),
dim,
order=mesh_order,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % h
],
force_ambient_dim=dim,
target_unit="MM")
logger.info("%d elements", mesh.nelements)
# {{{ discretizations and connections
from meshmode.discretization import Discretization
vol_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(quad_order))
from meshmode.discretization.connection import make_face_restriction
bdry_connection = make_face_restriction(
actx, vol_discr,
InterpolatoryQuadratureSimplexGroupFactory(quad_order), BTAG_ALL)
bdry_discr = bdry_connection.to_discr
# }}}
from math import gamma
true_surf = 2 * np.pi**(dim / 2) / gamma(dim / 2)
true_vol = true_surf / dim
vol_x = thaw(vol_discr.nodes(), actx)
vol_one = vol_x[0] * 0 + 1
from pytential import norm, integral # noqa
comp_vol = integral(vol_discr, vol_one)
rel_vol_err = abs(true_vol - comp_vol) / true_vol
vol_eoc_rec.add_data_point(h, rel_vol_err)
print("VOL", true_vol, comp_vol)
bdry_x = thaw(bdry_discr.nodes(), actx)
bdry_one_exact = bdry_x[0] * 0 + 1
bdry_one = bdry_connection(vol_one)
intp_err = norm(bdry_discr, bdry_one - bdry_one_exact)
assert intp_err < 1e-14
comp_surf = integral(bdry_discr, bdry_one)
rel_surf_err = abs(true_surf - comp_surf) / true_surf
surf_eoc_rec.add_data_point(h, rel_surf_err)
print("SURF", true_surf, comp_surf)
if visualize:
from meshmode.discretization.visualization import make_visualizer
vol_vis = make_visualizer(actx, vol_discr, 7)
bdry_vis = make_visualizer(actx, bdry_discr, 7)
name = src_file.split("-")[0]
vol_vis.write_vtk_file(f"sanity_balls_volume_{name}_{h:g}.vtu", [
("f", vol_one),
("area_el",
bind(vol_discr,
sym.area_element(mesh.ambient_dim,
mesh.ambient_dim))(actx)),
])
bdry_vis.write_vtk_file(f"sanity_balls_boundary_{name}_{h:g}.vtu",
[("f", bdry_one)])
# {{{ check normals point outward
normal_outward_check = bind(
bdry_discr,
sym.normal(mesh.ambient_dim) | sym.nodes(mesh.ambient_dim),
)(actx).as_scalar()
normal_outward_check = flatten_to_numpy(actx, normal_outward_check > 0)
assert normal_outward_check.all(), normal_outward_check
# }}}
print("---------------------------------")
print("VOLUME")
print("---------------------------------")
print(vol_eoc_rec)
assert vol_eoc_rec.order_estimate() >= mesh_order
print("---------------------------------")
print("SURFACE")
print("---------------------------------")
print(surf_eoc_rec)
assert surf_eoc_rec.order_estimate() >= mesh_order
def test_opposite_face_interpolation(actx_factory, group_factory, mesh_name,
dim, mesh_pars):
if (group_factory is LegendreGaussLobattoTensorProductGroupFactory
and mesh_name in ["segment", "blob"]):
pytest.skip("tensor products not implemented on blobs")
logging.basicConfig(level=logging.INFO)
actx = actx_factory()
if group_factory is LegendreGaussLobattoTensorProductGroupFactory:
group_cls = TensorProductElementGroup
else:
group_cls = SimplexElementGroup
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, make_opposite_face_connection, check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 5
def f(x):
return 0.1 * actx.np.sin(30 * x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "segment":
assert dim == 1
mesh = mgen.generate_box_mesh([np.linspace(-0.5, 0.5, mesh_par)],
order=order,
group_cls=group_cls)
h = 1.0 / mesh_par
elif mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"),
2,
order=order,
force_ambient_dim=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %s;" % h
],
target_unit="MM",
)
print("END GEN")
elif mesh_name == "warp":
mesh = mgen.generate_warped_rect_mesh(dim,
order=order,
nelements_side=mesh_par,
group_cls=group_cls)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(actx, mesh, group_factory(order))
print("h=%s -> %d elements" %
(h, sum(mgrp.nelements for mgrp in mesh.groups)))
bdry_connection = make_face_restriction(actx, vol_discr,
group_factory(order),
FACE_RESTR_INTERIOR)
bdry_discr = bdry_connection.to_discr
opp_face = make_opposite_face_connection(actx, bdry_connection)
check_connection(actx, opp_face)
bdry_x = thaw(bdry_discr.nodes()[0], actx)
bdry_f = f(bdry_x)
bdry_f_2 = opp_face(bdry_f)
err = flat_norm(bdry_f - bdry_f_2, np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1.7e-13)
def test_all_faces_interpolation(actx_factory, group_factory, mesh_name, dim,
mesh_pars, per_face_groups):
if (group_factory is LegendreGaussLobattoTensorProductGroupFactory
and mesh_name == "blob"):
pytest.skip("tensor products not implemented on blobs")
actx = actx_factory()
if group_factory is LegendreGaussLobattoTensorProductGroupFactory:
group_cls = TensorProductElementGroup
else:
group_cls = SimplexElementGroup
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, make_face_to_all_faces_embedding,
check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
def f(x):
return 0.1 * actx.np.sin(30 * x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"),
2,
order=order,
force_ambient_dim=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %s;" % h
],
target_unit="MM",
)
print("END GEN")
elif mesh_name == "warp":
mesh = mgen.generate_warped_rect_mesh(dim,
order=4,
nelements_side=mesh_par,
group_cls=group_cls)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(actx, mesh, group_factory(order))
print("h=%s -> %d elements" %
(h, sum(mgrp.nelements for mgrp in mesh.groups)))
all_face_bdry_connection = make_face_restriction(
actx,
vol_discr,
group_factory(order),
FACE_RESTR_ALL,
per_face_groups=per_face_groups)
all_face_bdry_discr = all_face_bdry_connection.to_discr
for ito_grp, ceg in enumerate(all_face_bdry_connection.groups):
for ibatch, batch in enumerate(ceg.batches):
assert np.array_equal(
actx.to_numpy(actx.thaw(batch.from_element_indices)),
np.arange(vol_discr.mesh.nelements))
if per_face_groups:
assert ito_grp == batch.to_element_face
else:
assert ibatch == batch.to_element_face
all_face_x = thaw(all_face_bdry_discr.nodes()[0], actx)
all_face_f = f(all_face_x)
all_face_f_2 = all_face_bdry_discr.zeros(actx)
for boundary_tag in [
BTAG_ALL,
FACE_RESTR_INTERIOR,
]:
bdry_connection = make_face_restriction(
actx,
vol_discr,
group_factory(order),
boundary_tag,
per_face_groups=per_face_groups)
bdry_discr = bdry_connection.to_discr
bdry_x = thaw(bdry_discr.nodes()[0], actx)
bdry_f = f(bdry_x)
all_face_embedding = make_face_to_all_faces_embedding(
actx, bdry_connection, all_face_bdry_discr)
check_connection(actx, all_face_embedding)
all_face_f_2 = all_face_f_2 + all_face_embedding(bdry_f)
err = flat_norm(all_face_f - all_face_f_2, np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-14)
def main():
# cl.array.to_device(queue, numpy_array)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("ellipsoid.step"),
2,
order=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
print("%d elements" % mesh.nelements)
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5 * (bbox_min + bbox_max)
bbox_size = max(bbox_max - bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr,
4 * target_order,
qbx_order,
fmm_order=qbx_order + 10,
fmm_backend="fmmlib")
from pytential.symbolic.pde.maxwell import MuellerAugmentedMFIEOperator
pde_op = MuellerAugmentedMFIEOperator(
omega=0.4,
epss=[1.4, 1.0],
mus=[1.2, 1.0],
)
from pytential import bind, sym
unk = pde_op.make_unknown("sigma")
sym_operator = pde_op.operator(unk)
sym_rhs = pde_op.rhs(sym.make_sym_vector("Einc", 3),
sym.make_sym_vector("Hinc", 3))
sym_repr = pde_op.representation(0, unk)
if 1:
expr = sym_repr
print(sym.pretty(expr))
print("#" * 80)
from pytential.target import PointsTarget
tgt_points = np.zeros((3, 1))
tgt_points[0, 0] = 100
tgt_points[1, 0] = -200
tgt_points[2, 0] = 300
bound_op = bind((qbx, PointsTarget(tgt_points)), expr)
print(bound_op.code)
if 1:
def green3e(x, y, z, source, strength, k):
# electric field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# E = (I + Hess)(exp(ikr)/r) dot (strength)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout = np.exp(1j * k * rr) / rr
evec = fout * strength
qmat = np.zeros((3, 3), dtype=np.complex128)
qmat[0, 0] = (2 * dx**2 - dy**2 - dz**2) * (1 - 1j * k * rr)
qmat[1, 1] = (2 * dy**2 - dz**2 - dx**2) * (1 - 1j * k * rr)
qmat[2, 2] = (2 * dz**2 - dx**2 - dy**2) * (1 - 1j * k * rr)
qmat[0, 0] = qmat[0, 0] + (-k**2 * dx**2 * rr**2)
qmat[1, 1] = qmat[1, 1] + (-k**2 * dy**2 * rr**2)
qmat[2, 2] = qmat[2, 2] + (-k**2 * dz**2 * rr**2)
qmat[0, 1] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dx * dy)
qmat[1, 2] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dy * dz)
qmat[2, 0] = (3 - k**2 * rr**2 - 3 * 1j * k * rr) * (dz * dx)
qmat[1, 0] = qmat[0, 1]
qmat[2, 1] = qmat[1, 2]
qmat[0, 2] = qmat[2, 0]
fout = np.exp(1j * k * rr) / rr**5 / k**2
fvec = fout * np.dot(qmat, strength)
evec = evec + fvec
return evec
def green3m(x, y, z, source, strength, k):
# magnetic field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# H = curl((I + Hess)(exp(ikr)/r) dot (strength)) =
# strength \cross \grad (exp(ikr)/r)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout = (1 - 1j * k * rr) * np.exp(1j * k * rr) / rr**3
fvec = np.zeros(3, dtype=np.complex128)
fvec[0] = fout * dx
fvec[1] = fout * dy
fvec[2] = fout * dz
hvec = np.cross(strength, fvec)
return hvec
def dipole3e(x, y, z, source, strength, k):
#
# evalaute electric and magnetic field due
# to monochromatic electric dipole located at "source"
# with intensity "strength"
evec = green3e(x, y, z, source, strength, k)
evec = evec * 1j * k
hvec = green3m(x, y, z, source, strength, k)
return evec, hvec
def dipole3m(x, y, z, source, strength, k):
#
# evalaute electric and magnetic field due
# to monochromatic magnetic dipole located at "source"
# with intensity "strength"
evec = green3m(x, y, z, source, strength, k)
hvec = green3e(x, y, z, source, strength, k)
hvec = -hvec * 1j * k
return evec, hvec
def dipole3eall(x, y, z, sources, strengths, k):
ns = len(strengths)
evec = np.zeros(3, dtype=np.complex128)
hvec = np.zeros(3, dtype=np.complex128)
for i in range(ns):
evect, hvect = dipole3e(x, y, z, sources[i], strengths[i], k)
evec = evec + evect
hvec = hvec + hvect
nodes = density_discr.nodes().with_queue(queue).get()
source = [0.01, -0.03, 0.02]
# source = cl.array.to_device(queue,np.zeros(3))
# source[0] = 0.01
# source[1] =-0.03
# source[2] = 0.02
strength = np.ones(3)
# evec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
# hvec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
evec = np.zeros((3, len(nodes[0])), dtype=np.complex128)
hvec = np.zeros((3, len(nodes[0])), dtype=np.complex128)
for i in range(len(nodes[0])):
evec[:, i], hvec[:, i] = dipole3e(nodes[0][i], nodes[1][i],
nodes[2][i], source, strength, k)
print(np.shape(hvec))
print(type(evec))
print(type(hvec))
evec = cl.array.to_device(queue, evec)
hvec = cl.array.to_device(queue, hvec)
bvp_rhs = bind(qbx, sym_rhs)(queue, Einc=evec, Hinc=hvec)
print(np.shape(bvp_rhs))
print(type(bvp_rhs))
# print(bvp_rhs)
1 / -1
bound_op = bind(qbx, sym_operator)
from pytential.solve import gmres
if 0:
gmres_result = gmres(bound_op.scipy_op(queue,
"sigma",
dtype=np.complex128,
k=k),
bvp_rhs,
tol=1e-8,
progress=True,
stall_iterations=0,
hard_failure=True)
sigma = gmres_result.solution
fld_at_tgt = bind((qbx, PointsTarget(tgt_points)),
sym_repr)(queue, sigma=bvp_rhs, k=k)
fld_at_tgt = np.array([fi.get() for fi in fld_at_tgt])
print(fld_at_tgt)
1 / 0
# }}}
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_normals = bind(density_discr, sym.normal(3))(queue)\
.as_vector(dtype=object)
bdry_vis.write_vtk_file("source.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
fplot = FieldPlotter(bbox_center,
extent=2 * bbox_size,
npoints=(150, 150, 1))
qbx_tgt_tol = qbx.copy(target_association_tolerance=0.1)
from pytential.target import PointsTarget
from pytential.qbx import QBXTargetAssociationFailedException
rho_sym = sym.var("rho")
try:
fld_in_vol = bind((qbx_tgt_tol, PointsTarget(fplot.points)),
sym.make_obj_array([
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None),
sym.d_dx(
3,
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dy(
3,
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dz(
3,
sym.S(pde_op.kernel,
rho_sym,
k=sym.var("k"),
qbx_forced_limit=None)),
]))(queue, jt=jt, rho=rho, k=k)
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file(
"failed-targets.vts",
[("failed_targets", e.failed_target_flags.get(queue))])
raise
fld_in_vol = sym.make_obj_array([fiv.get() for fiv in fld_in_vol])
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("potential.vts", [
("potential", fld_in_vol[0]),
("grad", fld_in_vol[1:]),
])
def test_sanity_balls(ctx_getter, src_file, dim, mesh_order,
visualize=False):
pytest.importorskip("pytential")
logging.basicConfig(level=logging.INFO)
ctx = ctx_getter()
queue = cl.CommandQueue(ctx)
from pytools.convergence import EOCRecorder
vol_eoc_rec = EOCRecorder()
surf_eoc_rec = EOCRecorder()
# overkill
quad_order = mesh_order
from pytential import bind, sym
for h in [0.2, 0.14, 0.1]:
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(src_file), dim, order=mesh_order,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h],
force_ambient_dim=dim)
logger.info("%d elements" % mesh.nelements)
# {{{ discretizations and connections
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
vol_discr = Discretization(ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(quad_order))
from meshmode.discretization.connection import make_boundary_restriction
bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction(
queue, vol_discr,
InterpolatoryQuadratureSimplexGroupFactory(quad_order))
# }}}
# {{{ visualizers
from meshmode.discretization.visualization import make_visualizer
vol_vis = make_visualizer(queue, vol_discr, 20)
bdry_vis = make_visualizer(queue, bdry_discr, 20)
# }}}
from math import gamma
true_surf = 2*np.pi**(dim/2)/gamma(dim/2)
true_vol = true_surf/dim
vol_x = vol_discr.nodes().with_queue(queue)
vol_one = vol_x[0].copy()
vol_one.fill(1)
from pytential import norm, integral # noqa
comp_vol = integral(vol_discr, queue, vol_one)
rel_vol_err = abs(true_vol - comp_vol) / true_vol
vol_eoc_rec.add_data_point(h, rel_vol_err)
print("VOL", true_vol, comp_vol)
bdry_x = bdry_discr.nodes().with_queue(queue)
bdry_one_exact = bdry_x[0].copy()
bdry_one_exact.fill(1)
bdry_one = bdry_connection(queue, vol_one).with_queue(queue)
intp_err = norm(bdry_discr, queue, bdry_one-bdry_one_exact)
assert intp_err < 1e-14
comp_surf = integral(bdry_discr, queue, bdry_one)
rel_surf_err = abs(true_surf - comp_surf) / true_surf
surf_eoc_rec.add_data_point(h, rel_surf_err)
print("SURF", true_surf, comp_surf)
if visualize:
vol_vis.write_vtk_file("volume-h=%g.vtu" % h, [
("f", vol_one),
("area_el", bind(vol_discr, sym.area_element())(queue)),
])
bdry_vis.write_vtk_file("boundary-h=%g.vtu" % h, [("f", bdry_one)])
# {{{ check normals point outward
normal_outward_check = bind(bdry_discr,
sym.normal() | sym.Nodes(),
)(queue).as_scalar() > 0
assert normal_outward_check.get().all(), normal_outward_check.get()
# }}}
print("---------------------------------")
print("VOLUME")
print("---------------------------------")
print(vol_eoc_rec)
assert vol_eoc_rec.order_estimate() >= mesh_order
print("---------------------------------")
print("SURFACE")
print("---------------------------------")
print(surf_eoc_rec)
assert surf_eoc_rec.order_estimate() >= mesh_order
def test_boundary_interpolation(ctx_getter, group_factory, boundary_tag,
mesh_name, dim, mesh_pars, per_face_groups):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (make_face_restriction,
check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
def f(x):
return 0.1 * cl.clmath.sin(30 * x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(FileSource("blob-2d.step"),
2,
order=order,
force_ambient_dim=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %s;" % h
])
print("END GEN")
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(cl_ctx, mesh, group_factory(order))
print("h=%s -> %d elements" %
(h, sum(mgrp.nelements for mgrp in mesh.groups)))
x = vol_discr.nodes()[0].with_queue(queue)
vol_f = f(x)
bdry_connection = make_face_restriction(
vol_discr,
group_factory(order),
boundary_tag,
per_face_groups=per_face_groups)
check_connection(bdry_connection)
bdry_discr = bdry_connection.to_discr
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
bdry_f_2 = bdry_connection(queue, vol_f)
if mesh_name == "blob" and dim == 2:
mat = bdry_connection.full_resample_matrix(queue).get(queue)
bdry_f_2_by_mat = mat.dot(vol_f.get())
mat_error = la.norm(bdry_f_2.get(queue=queue) - bdry_f_2_by_mat)
assert mat_error < 1e-14, mat_error
err = la.norm((bdry_f - bdry_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-14)
qbx_order = 2
nelements = 60
mode_nr = 0
h = 0.4
k = 0
if k:
kernel = HelmholtzKernel("k")
else:
kernel = LaplaceKernel()
#kernel = OneKernel()
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("molecule.step"), 2, order=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5*(bbox_min+bbox_max)
bbox_size = max(bbox_max-bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
def main(mesh_name="ellipsoid"):
import logging
logger = logging.getLogger(__name__)
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
if mesh_name == "ellipsoid":
cad_file_name = "geometries/ellipsoid.step"
h = 0.6
elif mesh_name == "two-cylinders":
cad_file_name = "geometries/two-cylinders-smooth.step"
h = 0.4
else:
raise ValueError("unknown mesh name: %s" % mesh_name)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(cad_file_name),
2,
order=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %g;" % h],
target_unit="MM")
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5 * (bbox_min + bbox_max)
bbox_size = max(bbox_max - bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
actx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr,
4 * target_order,
qbx_order,
fmm_order=qbx_order + 3,
target_association_tolerance=0.15)
from pytential.target import PointsTarget
fplot = FieldPlotter(bbox_center, extent=3.5 * bbox_size, npoints=150)
from pytential import GeometryCollection
places = GeometryCollection(
{
"qbx": qbx,
"targets": PointsTarget(fplot.points)
}, auto_where="qbx")
density_discr = places.get_discretization("qbx")
nodes = thaw(actx, density_discr.nodes())
angle = actx.np.arctan2(nodes[1], nodes[0])
if k:
kernel = HelmholtzKernel(3)
else:
kernel = LaplaceKernel(3)
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None))
op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = actx.np.cos(mode_nr * angle)
if 0:
from meshmode.dof_array import flatten, unflatten
sigma = flatten(0 * angle)
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
sigma = unflatten(actx, density_discr, sigma)
if isinstance(kernel, HelmholtzKernel):
for i, elem in np.ndenumerate(sigma):
sigma[i] = elem.astype(np.complex128)
fld_in_vol = actx.to_numpy(
bind(places, op, auto_where=("qbx", "targets"))(actx, sigma=sigma,
k=k))
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file("layerpot-3d-potential.vts",
[("potential", fld_in_vol)])
bdry_normals = bind(places, sym.normal(
density_discr.ambient_dim))(actx).as_vector(dtype=object)
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(actx, density_discr, target_order)
bdry_vis.write_vtk_file("layerpot-3d-density.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/a869fc3/"
"surface-3d/betterplane.brep")
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
mesh = generate_gmsh(
ScriptWithFilesSource("""
Merge "betterplane.brep";
Mesh.CharacteristicLengthMax = %(lcmax)f;
Mesh.ElementOrder = 2;
Mesh.CharacteristicLengthExtendFromBoundary = 0;
// 2D mesh optimization
// Mesh.Lloyd = 1;
l_superfine() = Unique(Abs(Boundary{ Surface{
27, 25, 17, 13, 18 }; }));
l_fine() = Unique(Abs(Boundary{ Surface{ 2, 6, 7}; }));
l_coarse() = Unique(Abs(Boundary{ Surface{ 14, 16 }; }));
// p() = Unique(Abs(Boundary{ Line{l_fine()}; }));
// Characteristic Length{p()} = 0.05;
Field[1] = Attractor;
Field[1].NNodesByEdge = 100;
Field[1].EdgesList = {l_superfine()};
Field[2] = Threshold;
Field[2].IField = 1;
Field[2].LcMin = 0.075;
Field[2].LcMax = %(lcmax)f;
Field[2].DistMin = 0.1;
Field[2].DistMax = 0.4;
Field[3] = Attractor;
Field[3].NNodesByEdge = 100;
Field[3].EdgesList = {l_fine()};
Field[4] = Threshold;
Field[4].IField = 3;
Field[4].LcMin = 0.1;
Field[4].LcMax = %(lcmax)f;
Field[4].DistMin = 0.15;
Field[4].DistMax = 0.4;
Field[5] = Attractor;
Field[5].NNodesByEdge = 100;
Field[5].EdgesList = {l_coarse()};
Field[6] = Threshold;
Field[6].IField = 5;
Field[6].LcMin = 0.15;
Field[6].LcMax = %(lcmax)f;
Field[6].DistMin = 0.2;
Field[6].DistMax = 0.4;
Field[7] = Min;
Field[7].FieldsList = {2, 4, 6};
Background Field = 7;
""" % {
"lcmax": resolution,
}, ["betterplane.brep"]), 2)
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
from meshmode.mesh.io import generate_gmsh, FileSource
h = 0.3
order = 1
mesh = generate_gmsh(
FileSource("../test/blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
from meshmode.mesh.visualization import mesh_to_tikz
print(mesh_to_tikz(mesh))
def test_boundary_interpolation(ctx_getter, group_factory, boundary_tag,
mesh_name, dim, mesh_pars, per_face_groups):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
def f(x):
return 0.1*cl.clmath.sin(30*x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
print("END GEN")
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1/mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(cl_ctx, mesh,
group_factory(order))
print("h=%s -> %d elements" % (
h, sum(mgrp.nelements for mgrp in mesh.groups)))
x = vol_discr.nodes()[0].with_queue(queue)
vol_f = f(x)
bdry_connection = make_face_restriction(
vol_discr, group_factory(order),
boundary_tag, per_face_groups=per_face_groups)
check_connection(bdry_connection)
bdry_discr = bdry_connection.to_discr
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
bdry_f_2 = bdry_connection(queue, vol_f)
if mesh_name == "blob" and dim == 2:
mat = bdry_connection.full_resample_matrix(queue).get(queue)
bdry_f_2_by_mat = mat.dot(vol_f.get())
mat_error = la.norm(bdry_f_2.get(queue=queue) - bdry_f_2_by_mat)
assert mat_error < 1e-14, mat_error
err = la.norm((bdry_f-bdry_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (
eoc_rec.order_estimate() >= order-0.5
or eoc_rec.max_error() < 1e-14)
def main():
# cl.array.to_device(queue, numpy_array)
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("ellipsoid.step"), 2, order=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
print("%d elements" % mesh.nelements)
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5*(bbox_min+bbox_max)
bbox_size = max(bbox_max-bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 10, fmm_backend="fmmlib")
from pytential.symbolic.pde.maxwell import MuellerAugmentedMFIEOperator
pde_op = MuellerAugmentedMFIEOperator(
omega=0.4,
epss=[1.4, 1.0],
mus=[1.2, 1.0],
)
from pytential import bind, sym
unk = pde_op.make_unknown("sigma")
sym_operator = pde_op.operator(unk)
sym_rhs = pde_op.rhs(
sym.make_sym_vector("Einc", 3),
sym.make_sym_vector("Hinc", 3))
sym_repr = pde_op.representation(0, unk)
if 1:
expr = sym_repr
print(sym.pretty(expr))
print("#"*80)
from pytential.target import PointsTarget
tgt_points=np.zeros((3,1))
tgt_points[0,0] = 100
tgt_points[1,0] = -200
tgt_points[2,0] = 300
bound_op = bind((qbx, PointsTarget(tgt_points)), expr)
print(bound_op.code)
if 1:
def green3e(x,y,z,source,strength,k):
# electric field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# E = (I + Hess)(exp(ikr)/r) dot (strength)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout = np.exp(1j*k*rr)/rr
evec = fout*strength
qmat = np.zeros((3,3),dtype=np.complex128)
qmat[0,0]=(2*dx**2-dy**2-dz**2)*(1-1j*k*rr)
qmat[1,1]=(2*dy**2-dz**2-dx**2)*(1-1j*k*rr)
qmat[2,2]=(2*dz**2-dx**2-dy**2)*(1-1j*k*rr)
qmat[0,0]=qmat[0,0]+(-k**2*dx**2*rr**2)
qmat[1,1]=qmat[1,1]+(-k**2*dy**2*rr**2)
qmat[2,2]=qmat[2,2]+(-k**2*dz**2*rr**2)
qmat[0,1]=(3-k**2*rr**2-3*1j*k*rr)*(dx*dy)
qmat[1,2]=(3-k**2*rr**2-3*1j*k*rr)*(dy*dz)
qmat[2,0]=(3-k**2*rr**2-3*1j*k*rr)*(dz*dx)
qmat[1,0]=qmat[0,1]
qmat[2,1]=qmat[1,2]
qmat[0,2]=qmat[2,0]
fout=np.exp(1j*k*rr)/rr**5/k**2
fvec = fout*np.dot(qmat,strength)
evec = evec + fvec
return evec
def green3m(x,y,z,source,strength,k):
# magnetic field corresponding to dyadic green's function
# due to monochromatic electric dipole located at "source".
# "strength" is the the intensity of the dipole.
# H = curl((I + Hess)(exp(ikr)/r) dot (strength)) =
# strength \cross \grad (exp(ikr)/r)
#
dx = x - source[0]
dy = y - source[1]
dz = z - source[2]
rr = np.sqrt(dx**2 + dy**2 + dz**2)
fout=(1-1j*k*rr)*np.exp(1j*k*rr)/rr**3
fvec = np.zeros(3,dtype=np.complex128)
fvec[0] = fout*dx
fvec[1] = fout*dy
fvec[2] = fout*dz
hvec = np.cross(strength,fvec)
return hvec
def dipole3e(x,y,z,source,strength,k):
#
# evalaute electric and magnetic field due
# to monochromatic electric dipole located at "source"
# with intensity "strength"
evec = green3e(x,y,z,source,strength,k)
evec = evec*1j*k
hvec = green3m(x,y,z,source,strength,k)
return evec,hvec
def dipole3m(x,y,z,source,strength,k):
#
# evalaute electric and magnetic field due
# to monochromatic magnetic dipole located at "source"
# with intensity "strength"
evec = green3m(x,y,z,source,strength,k)
hvec = green3e(x,y,z,source,strength,k)
hvec = -hvec*1j*k
return evec,hvec
def dipole3eall(x,y,z,sources,strengths,k):
ns = len(strengths)
evec = np.zeros(3,dtype=np.complex128)
hvec = np.zeros(3,dtype=np.complex128)
for i in range(ns):
evect,hvect = dipole3e(x,y,z,sources[i],strengths[i],k)
evec = evec + evect
hvec = hvec + hvect
nodes = density_discr.nodes().with_queue(queue).get()
source = [0.01,-0.03,0.02]
# source = cl.array.to_device(queue,np.zeros(3))
# source[0] = 0.01
# source[1] =-0.03
# source[2] = 0.02
strength = np.ones(3)
# evec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
# hvec = cl.array.to_device(queue,np.zeros((3,len(nodes[0])),dtype=np.complex128))
evec = np.zeros((3,len(nodes[0])),dtype=np.complex128)
hvec = np.zeros((3,len(nodes[0])),dtype=np.complex128)
for i in range(len(nodes[0])):
evec[:,i],hvec[:,i] = dipole3e(nodes[0][i],nodes[1][i],nodes[2][i],source,strength,k)
print(np.shape(hvec))
print(type(evec))
print(type(hvec))
evec = cl.array.to_device(queue,evec)
hvec = cl.array.to_device(queue,hvec)
bvp_rhs = bind(qbx, sym_rhs)(queue,Einc=evec,Hinc=hvec)
print(np.shape(bvp_rhs))
print(type(bvp_rhs))
# print(bvp_rhs)
1/-1
bound_op = bind(qbx, sym_operator)
from pytential.solve import gmres
if 0:
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma", dtype=np.complex128, k=k),
bvp_rhs, tol=1e-8, progress=True,
stall_iterations=0,
hard_failure=True)
sigma = gmres_result.solution
fld_at_tgt = bind((qbx, PointsTarget(tgt_points)), sym_repr)(queue,
sigma=bvp_rhs,k=k)
fld_at_tgt = np.array([
fi.get() for fi in fld_at_tgt
])
print(fld_at_tgt)
1/0
# }}}
#mlab.figure(bgcolor=(1, 1, 1))
if 1:
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_normals = bind(density_discr, sym.normal(3))(queue)\
.as_vector(dtype=object)
bdry_vis.write_vtk_file("source.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
fplot = FieldPlotter(bbox_center, extent=2*bbox_size, npoints=(150, 150, 1))
qbx_tgt_tol = qbx.copy(target_association_tolerance=0.1)
from pytential.target import PointsTarget
from pytential.qbx import QBXTargetAssociationFailedException
rho_sym = sym.var("rho")
try:
fld_in_vol = bind(
(qbx_tgt_tol, PointsTarget(fplot.points)),
sym.make_obj_array([
sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None),
sym.d_dx(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dy(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
sym.d_dz(3, sym.S(pde_op.kernel, rho_sym, k=sym.var("k"),
qbx_forced_limit=None)),
])
)(queue, jt=jt, rho=rho, k=k)
except QBXTargetAssociationFailedException as e:
fplot.write_vtk_file(
"failed-targets.vts",
[
("failed_targets", e.failed_target_flags.get(queue))
])
raise
fld_in_vol = sym.make_obj_array(
[fiv.get() for fiv in fld_in_vol])
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential.vts",
[
("potential", fld_in_vol[0]),
("grad", fld_in_vol[1:]),
]
)
def test_all_faces_interpolation(ctx_getter, mesh_name, dim, mesh_pars,
per_face_groups):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, make_face_to_all_faces_embedding,
check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
def f(x):
return 0.1*cl.clmath.sin(30*x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(
FileSource("blob-2d.step"), 2, order=order,
force_ambient_dim=2,
other_options=[
"-string", "Mesh.CharacteristicLengthMax = %s;" % h]
)
print("END GEN")
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1/mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(cl_ctx, mesh,
PolynomialWarpAndBlendGroupFactory(order))
print("h=%s -> %d elements" % (
h, sum(mgrp.nelements for mgrp in mesh.groups)))
all_face_bdry_connection = make_face_restriction(
vol_discr, PolynomialWarpAndBlendGroupFactory(order),
FRESTR_ALL_FACES, per_face_groups=per_face_groups)
all_face_bdry_discr = all_face_bdry_connection.to_discr
for ito_grp, ceg in enumerate(all_face_bdry_connection.groups):
for ibatch, batch in enumerate(ceg.batches):
assert np.array_equal(
batch.from_element_indices.get(queue),
np.arange(vol_discr.mesh.nelements))
if per_face_groups:
assert ito_grp == batch.to_element_face
else:
assert ibatch == batch.to_element_face
all_face_x = all_face_bdry_discr.nodes()[0].with_queue(queue)
all_face_f = f(all_face_x)
all_face_f_2 = all_face_bdry_discr.zeros(queue)
for boundary_tag in [
BTAG_ALL,
FRESTR_INTERIOR_FACES,
]:
bdry_connection = make_face_restriction(
vol_discr, PolynomialWarpAndBlendGroupFactory(order),
boundary_tag, per_face_groups=per_face_groups)
bdry_discr = bdry_connection.to_discr
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
all_face_embedding = make_face_to_all_faces_embedding(
bdry_connection, all_face_bdry_discr)
check_connection(all_face_embedding)
all_face_f_2 += all_face_embedding(queue, bdry_f)
err = la.norm((all_face_f-all_face_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (
eoc_rec.order_estimate() >= order-0.5
or eoc_rec.max_error() < 1e-14)
def main():
import logging
logging.basicConfig(level=logging.INFO)
ctx = cl.create_some_context()
queue = cl.CommandQueue(ctx)
mesh = generate_gmsh(
FileSource("circle.step"), 2, order=mesh_order,
force_ambient_dim=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h]
)
logger.info("%d elements" % mesh.nelements)
# {{{ discretizations and connections
vol_discr = Discretization(ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(vol_quad_order))
ovsmp_vol_discr = Discretization(ctx, mesh,
InterpolatoryQuadratureSimplexGroupFactory(vol_ovsmp_quad_order))
from meshmode.discretization.connection import (
make_boundary_restriction, make_same_mesh_connection)
bdry_mesh, bdry_discr, bdry_connection = make_boundary_restriction(
queue, vol_discr,
InterpolatoryQuadratureSimplexGroupFactory(bdry_quad_order))
vol_to_ovsmp_vol = make_same_mesh_connection(
queue, ovsmp_vol_discr, vol_discr)
# }}}
# {{{ visualizers
vol_vis = make_visualizer(queue, vol_discr, 20)
bdry_vis = make_visualizer(queue, bdry_discr, 20)
# }}}
vol_x = vol_discr.nodes().with_queue(queue)
ovsmp_vol_x = ovsmp_vol_discr.nodes().with_queue(queue)
rhs = rhs_func(vol_x[0], vol_x[1])
poisson_true_sol = sol_func(vol_x[0], vol_x[1])
vol_vis.write_vtk_file("volume.vtu", [("f", rhs)])
bdry_normals = bind(bdry_discr, p.normal())(queue).as_vector(dtype=object)
bdry_vis.write_vtk_file("boundary.vtu", [
("normals", bdry_normals)
])
bdry_nodes = bdry_discr.nodes().with_queue(queue)
bdry_f = rhs_func(bdry_nodes[0], bdry_nodes[1])
bdry_f_2 = bdry_connection(queue, rhs)
bdry_vis.write_vtk_file("y.vtu", [("f", bdry_f_2)])
if 0:
vol_vis.show_scalar_in_mayavi(rhs, do_show=False)
bdry_vis.show_scalar_in_mayavi(bdry_f - bdry_f_2, line_width=10,
do_show=False)
import mayavi.mlab as mlab
mlab.colorbar()
mlab.show()
# {{{ compute volume potential
from sumpy.qbx import LayerPotential
from sumpy.expansion.local import LineTaylorLocalExpansion
def get_kernel():
from sumpy.symbolic import pymbolic_real_norm_2
from pymbolic.primitives import (make_sym_vector, Variable as var)
r = pymbolic_real_norm_2(make_sym_vector("d", 3))
expr = var("log")(r)
scaling = 1/(2*var("pi"))
from sumpy.kernel import ExpressionKernel
return ExpressionKernel(
dim=3,
expression=expr,
scaling=scaling,
is_complex_valued=False)
laplace_2d_in_3d_kernel = get_kernel()
layer_pot = LayerPotential(ctx, [
LineTaylorLocalExpansion(laplace_2d_in_3d_kernel,
order=vol_qbx_order)])
targets = cl.array.zeros(queue, (3,) + vol_x.shape[1:], vol_x.dtype)
targets[:2] = vol_x
center_dist = np.min(
cl.clmath.sqrt(
bind(vol_discr, p.area_element())(queue)).get())
centers = make_obj_array([ci.copy().reshape(vol_discr.nnodes) for ci in targets])
centers[2][:] = center_dist
sources = cl.array.zeros(queue, (3,) + ovsmp_vol_x.shape[1:], ovsmp_vol_x.dtype)
sources[:2] = ovsmp_vol_x
ovsmp_rhs = vol_to_ovsmp_vol(queue, rhs)
ovsmp_vol_weights = bind(ovsmp_vol_discr, p.area_element() * p.QWeight())(queue)
evt, (vol_pot,) = layer_pot(
queue,
targets=targets.reshape(3, vol_discr.nnodes),
centers=centers,
sources=sources.reshape(3, ovsmp_vol_discr.nnodes),
strengths=(
(ovsmp_vol_weights*ovsmp_rhs).reshape(ovsmp_vol_discr.nnodes),)
)
vol_pot_bdry = bdry_connection(queue, vol_pot)
# }}}
# {{{ solve bvp
from sumpy.kernel import LaplaceKernel
from pytential.symbolic.pde.scalar import DirichletOperator
op = DirichletOperator(LaplaceKernel(2), -1, use_l2_weighting=True)
sym_sigma = sym.var("sigma")
op_sigma = op.operator(sym_sigma)
from pytential.qbx import QBXLayerPotentialSource
qbx = QBXLayerPotentialSource(
bdry_discr, fine_order=bdry_ovsmp_quad_order, qbx_order=qbx_order,
fmm_order=fmm_order
)
bound_op = bind(qbx, op_sigma)
poisson_bc = poisson_bc_func(bdry_nodes[0], bdry_nodes[1])
bvp_bc = poisson_bc - vol_pot_bdry
bdry_f = rhs_func(bdry_nodes[0], bdry_nodes[1])
bvp_rhs = bind(bdry_discr, op.prepare_rhs(sym.var("bc")))(queue, bc=bvp_bc)
from pytential.solve import gmres
gmres_result = gmres(
bound_op.scipy_op(queue, "sigma"),
bvp_rhs, tol=1e-14, progress=True,
hard_failure=False)
sigma = gmres_result.solution
print("gmres state:", gmres_result.state)
# }}}
bvp_sol = bind(
(qbx, vol_discr),
op.representation(sym_sigma))(queue, sigma=sigma)
poisson_sol = bvp_sol + vol_pot
poisson_err = poisson_sol-poisson_true_sol
rel_err = (
norm(vol_discr, queue, poisson_err)
/
norm(vol_discr, queue, poisson_true_sol))
bdry_vis.write_vtk_file("poisson-boundary.vtu", [
("vol_pot_bdry", vol_pot_bdry),
("sigma", sigma),
])
vol_vis.write_vtk_file("poisson-volume.vtu", [
("bvp_sol", bvp_sol),
("poisson_sol", poisson_sol),
("poisson_true_sol", poisson_true_sol),
("poisson_err", poisson_err),
("vol_pot", vol_pot),
("rhs", rhs),
])
print("h = %s" % h)
print("mesh_order = %s" % mesh_order)
print("vol_quad_order = %s" % vol_quad_order)
print("vol_ovsmp_quad_order = %s" % vol_ovsmp_quad_order)
print("bdry_quad_order = %s" % bdry_quad_order)
print("bdry_ovsmp_quad_order = %s" % bdry_ovsmp_quad_order)
print("qbx_order = %s" % qbx_order)
print("vol_qbx_order = %s" % vol_qbx_order)
print("fmm_order = %s" % fmm_order)
print()
print("rel err: %g" % rel_err)
def test_all_faces_interpolation(ctx_getter, mesh_name, dim, mesh_pars,
per_face_groups):
cl_ctx = ctx_getter()
queue = cl.CommandQueue(cl_ctx)
from meshmode.discretization import Discretization
from meshmode.discretization.connection import (
make_face_restriction, make_face_to_all_faces_embedding,
check_connection)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
order = 4
def f(x):
return 0.1 * cl.clmath.sin(30 * x)
for mesh_par in mesh_pars:
# {{{ get mesh
if mesh_name == "blob":
assert dim == 2
h = mesh_par
from meshmode.mesh.io import generate_gmsh, FileSource
print("BEGIN GEN")
mesh = generate_gmsh(FileSource("blob-2d.step"),
2,
order=order,
force_ambient_dim=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %s;" % h
])
print("END GEN")
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# }}}
vol_discr = Discretization(cl_ctx, mesh,
PolynomialWarpAndBlendGroupFactory(order))
print("h=%s -> %d elements" %
(h, sum(mgrp.nelements for mgrp in mesh.groups)))
all_face_bdry_connection = make_face_restriction(
vol_discr,
PolynomialWarpAndBlendGroupFactory(order),
FRESTR_ALL_FACES,
per_face_groups=per_face_groups)
all_face_bdry_discr = all_face_bdry_connection.to_discr
for ito_grp, ceg in enumerate(all_face_bdry_connection.groups):
for ibatch, batch in enumerate(ceg.batches):
assert np.array_equal(batch.from_element_indices.get(queue),
np.arange(vol_discr.mesh.nelements))
if per_face_groups:
assert ito_grp == batch.to_element_face
else:
assert ibatch == batch.to_element_face
all_face_x = all_face_bdry_discr.nodes()[0].with_queue(queue)
all_face_f = f(all_face_x)
all_face_f_2 = all_face_bdry_discr.zeros(queue)
for boundary_tag in [
BTAG_ALL,
FRESTR_INTERIOR_FACES,
]:
bdry_connection = make_face_restriction(
vol_discr,
PolynomialWarpAndBlendGroupFactory(order),
boundary_tag,
per_face_groups=per_face_groups)
bdry_discr = bdry_connection.to_discr
bdry_x = bdry_discr.nodes()[0].with_queue(queue)
bdry_f = f(bdry_x)
all_face_embedding = make_face_to_all_faces_embedding(
bdry_connection, all_face_bdry_discr)
check_connection(all_face_embedding)
all_face_f_2 += all_face_embedding(queue, bdry_f)
err = la.norm((all_face_f - all_face_f_2).get(), np.inf)
eoc_rec.add_data_point(h, err)
print(eoc_rec)
assert (eoc_rec.order_estimate() >= order - 0.5
or eoc_rec.max_error() < 1e-14)
def main():
import logging
logger = logging.getLogger(__name__)
logging.basicConfig(level=logging.WARNING) # INFO for more progress info
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource(cad_file_name), 2, order=2,
other_options=["-string", "Mesh.CharacteristicLengthMax = %g;" % h])
from meshmode.mesh.processing import perform_flips
# Flip elements--gmsh generates inside-out geometry.
mesh = perform_flips(mesh, np.ones(mesh.nelements))
from meshmode.mesh.processing import find_bounding_box
bbox_min, bbox_max = find_bounding_box(mesh)
bbox_center = 0.5*(bbox_min+bbox_max)
bbox_size = max(bbox_max-bbox_min) / 2
logger.info("%d elements" % mesh.nelements)
from pytential.qbx import QBXLayerPotentialSource
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
density_discr = Discretization(
cl_ctx, mesh, InterpolatoryQuadratureSimplexGroupFactory(target_order))
qbx, _ = QBXLayerPotentialSource(density_discr, 4*target_order, qbx_order,
fmm_order=qbx_order + 3,
target_association_tolerance=0.15).with_refinement()
nodes = density_discr.nodes().with_queue(queue)
angle = cl.clmath.atan2(nodes[1], nodes[0])
from pytential import bind, sym
#op = sym.d_dx(sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None))
op = sym.D(kernel, sym.var("sigma"), qbx_forced_limit=None)
#op = sym.S(kernel, sym.var("sigma"), qbx_forced_limit=None)
sigma = cl.clmath.cos(mode_nr*angle)
if 0:
sigma = 0*angle
from random import randrange
for i in range(5):
sigma[randrange(len(sigma))] = 1
if isinstance(kernel, HelmholtzKernel):
sigma = sigma.astype(np.complex128)
fplot = FieldPlotter(bbox_center, extent=3.5*bbox_size, npoints=150)
from pytential.target import PointsTarget
fld_in_vol = bind(
(qbx, PointsTarget(fplot.points)),
op)(queue, sigma=sigma, k=k).get()
#fplot.show_scalar_in_mayavi(fld_in_vol.real, max_val=5)
fplot.write_vtk_file(
"potential-3d.vts",
[
("potential", fld_in_vol)
]
)
bdry_normals = bind(
density_discr,
sym.normal(density_discr.ambient_dim))(queue).as_vector(dtype=object)
from meshmode.discretization.visualization import make_visualizer
bdry_vis = make_visualizer(queue, density_discr, target_order)
bdry_vis.write_vtk_file("source-3d.vtu", [
("sigma", sigma),
("bdry_normals", bdry_normals),
])
from meshmode.mesh.io import generate_gmsh, FileSource
from meshmode.mesh.visualization import mesh_to_tikz
h = 0.3
order = 1
mesh = generate_gmsh(
FileSource("../test/blob-2d.step"),
2,
order=order,
force_ambient_dim=2,
other_options=["-string",
"Mesh.CharacteristicLengthMax = %s;" % h])
print(mesh_to_tikz(mesh))