def make_cylinder_mesh(radius=0.5, height=1, radial_subdivisions=10,
height_subdivisions=1, max_volume=None, periodic=False,
boundary_tagger=(lambda fvi, el, fn, all_v: [])):
from meshpy.tet import MeshInfo, build
from meshpy.geometry import make_cylinder
points, facets, facet_holestarts, facet_markers = \
make_cylinder(radius, height, radial_subdivisions,
height_subdivisions)
assert len(facets) == len(facet_markers)
if periodic:
return _make_z_periodic_mesh(
points, facets, facet_holestarts, facet_markers,
height=height,
max_volume=max_volume,
boundary_tagger=boundary_tagger)
else:
mesh_info = MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets_ex(facets, facet_holestarts, facet_markers)
generated_mesh = build(mesh_info, max_volume=max_volume)
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Tetrahedron
vertices = numpy.asarray(generated_mesh.points, dtype=float, order="C")
return make_conformal_mesh_ext(
vertices,
[Tetrahedron(i, el_idx, vertices)
for i, el_idx in enumerate(generated_mesh.elements)],
boundary_tagger)
def make_1d_mesh(points, left_tag=None, right_tag=None, periodic=False,
boundary_tagger=None, volume_tagger=None):
def my_boundary_tagger(fvi, el, fn, all_v):
if el.face_normals[fn][0] < 0:
return [left_tag]
else:
return [right_tag]
kwargs = {}
if volume_tagger is not None:
kwargs["volume_tagger"] = volume_tagger
if periodic:
left_tag = "x_minus"
right_tag = "x_plus"
kwargs["periodicity"] = [(left_tag, right_tag)]
if boundary_tagger is not None:
raise ValueError("cannot have both periodicity and a custom "
"boundary tagger")
boundary_tagger = my_boundary_tagger
else:
boundary_tagger = boundary_tagger or my_boundary_tagger
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(points, order="C").reshape((len(points), 1))
from hedge.mesh.element import Interval
return make_conformal_mesh_ext(
vertices,
[Interval(i, (i, i+1), vertices) for i in xrange(len(points)-1)],
boundary_tagger=boundary_tagger,
**kwargs)
def make_disk_mesh(r=0.5, faces=50, max_area=4e-3,
boundary_tagger=(lambda fvi, el, fn, all_v: [])):
from math import cos, sin, pi
def needs_refinement(vertices, area):
return area > max_area
points = [(r*cos(angle), r*sin(angle))
for angle in numpy.linspace(0, 2*pi, faces, endpoint=False)]
import meshpy.triangle as triangle
mesh_info = triangle.MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets(
list(_round_trip_connect(0, faces-1)),
faces*[1]
)
generated_mesh = triangle.build(mesh_info, refinement_func=needs_refinement)
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Triangle
vertices = numpy.asarray(generated_mesh.points, dtype=float, order="C")
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(generated_mesh.elements)],
boundary_tagger)
def make_mesh(a, b, pml_width=0.25, **kwargs):
from meshpy.geometry import GeometryBuilder, make_circle
geob = GeometryBuilder()
circle_centers = [(-1.5, 0), (1.5, 0)]
for cent in circle_centers:
geob.add_geometry(*make_circle(1, cent))
geob.wrap_in_box(1)
geob.wrap_in_box(pml_width)
mesh_mod = geob.mesher_module()
mi = mesh_mod.MeshInfo()
geob.set(mi)
mi.set_holes(circle_centers)
built_mi = mesh_mod.build(mi, **kwargs)
def boundary_tagger(fvi, el, fn, points):
return []
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Triangle
pts = np.asarray(built_mi.points, dtype=np.float64)
return make_conformal_mesh_ext(
pts,
[Triangle(i, el, pts)
for i, el in enumerate(built_mi.elements)],
boundary_tagger)
def make_mesh(a, b, pml_width=0.25, **kwargs):
from meshpy.geometry import GeometryBuilder, make_circle
geob = GeometryBuilder()
circle_centers = [(-1.5, 0), (1.5, 0)]
for cent in circle_centers:
geob.add_geometry(*make_circle(1, cent))
geob.wrap_in_box(1)
geob.wrap_in_box(pml_width)
mesh_mod = geob.mesher_module()
mi = mesh_mod.MeshInfo()
geob.set(mi)
mi.set_holes(circle_centers)
built_mi = mesh_mod.build(mi, **kwargs)
def boundary_tagger(fvi, el, fn, points):
return []
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Triangle
pts = np.asarray(built_mi.points, dtype=np.float64)
return make_conformal_mesh_ext(
pts, [Triangle(i, el, pts) for i, el in enumerate(built_mi.elements)],
boundary_tagger)
def finish_2d_rect_mesh(points, facets, facet_markers, marker2tag, refine_func,
periodicity, boundary_tagger):
"""Semi-internal bottom-half routine for generation of rectangular 2D meshes."""
import meshpy.triangle as triangle
mesh_info = triangle.MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets(facets, facet_markers)
#triangle.write_gnuplot_mesh("mesh.dat", mesh_info, True)
if periodicity is None:
periodicity = (False, False)
axes = ["x", "y"]
mesh_periodicity = []
periodic_tags = set()
for i, axis in enumerate(axes):
if periodicity[i]:
minus_tag = "minus_"+axis
plus_tag = "plus_"+axis
mesh_periodicity.append((minus_tag, plus_tag))
periodic_tags.add(minus_tag)
periodic_tags.add(plus_tag)
else:
mesh_periodicity.append(None)
generated_mesh = triangle.build(mesh_info,
refinement_func=refine_func,
allow_boundary_steiner=not (periodicity[0] or periodicity[1]))
fmlookup = MeshPyFaceMarkerLookup(generated_mesh)
def wrapped_boundary_tagger(fvi, el, fn, all_v):
btag = marker2tag[fmlookup(fvi)]
if btag in periodic_tags:
return [btag]
else:
return [btag] + boundary_tagger(fvi, el, fn, all_v)
vertices = numpy.asarray(generated_mesh.points, dtype=float, order="C")
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(generated_mesh.elements)],
wrapped_boundary_tagger,
periodicity=mesh_periodicity)
def _make_z_periodic_mesh(points, facets, facet_holestarts, facet_markers, height,
max_volume, boundary_tagger):
from meshpy.tet import MeshInfo, build
from meshpy.geometry import Marker
mesh_info = MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets_ex(facets, facet_holestarts, facet_markers)
mesh_info.pbc_groups.resize(1)
pbcg = mesh_info.pbc_groups[0]
pbcg.facet_marker_1 = Marker.MINUS_Z
pbcg.facet_marker_2 = Marker.PLUS_Z
pbcg.set_transform(translation=[0, 0, height])
def zper_boundary_tagger(fvi, el, fn, all_v):
# we only ask about *boundaries*
# we should not try to have the user tag
# the (periodicity-induced) interior faces
face_marker = fvi2fm[frozenset(fvi)]
if face_marker == Marker.MINUS_Z:
return ["minus_z"]
if face_marker == Marker.PLUS_Z:
return ["plus_z"]
result = boundary_tagger(fvi, el, fn, all_v)
if face_marker == Marker.SHELL:
result.append("shell")
return result
generated_mesh = build(mesh_info, max_volume=max_volume)
fvi2fm = generated_mesh.face_vertex_indices_to_face_marker
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Tetrahedron
vertices = numpy.asarray(generated_mesh.points, dtype=float, order="C")
return make_conformal_mesh_ext(
vertices,
[Tetrahedron(i, el_idx, vertices)
for i, el_idx in enumerate(generated_mesh.elements)],
zper_boundary_tagger,
periodicity=[None, None, ("minus_z", "plus_z")])
def make_ball_mesh(r=0.5, subdivisions=10, max_volume=None,
boundary_tagger=(lambda fvi, el, fn, all_v: [])):
from meshpy.tet import MeshInfo, build
from meshpy.geometry import make_ball
points, facets, facet_holestarts, facet_markers = \
make_ball(r, subdivisions)
mesh_info = MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets_ex(facets, facet_holestarts, facet_markers)
generated_mesh = build(mesh_info, max_volume=max_volume)
vertices = numpy.asarray(generated_mesh.points, dtype=float, order="C")
from hedge.mesh.element import Tetrahedron
from hedge.mesh import make_conformal_mesh_ext
return make_conformal_mesh_ext(
vertices,
[Tetrahedron(i, el_idx, vertices)
for i, el_idx in enumerate(generated_mesh.elements)],
boundary_tagger)
def make_extrusion_with_fine_core(rz,
inner_r,
max_volume_inner=1e-4,
max_volume_outer=5e-2,
radial_subdiv=20):
min_z = min(rz_pt[1] for rz_pt in rz)
max_z = max(rz_pt[1] for rz_pt in rz)
from meshpy.tet import MeshInfo, build
from meshpy.geometry import generate_surface_of_revolution
MINUS_Z_MARKER = 1
PLUS_Z_MARKER = 2
inner_points, inner_facets, inner_holes, inner_markers = \
generate_surface_of_revolution(
[
(0, min_z),
(inner_r, min_z),
(inner_r, max_z),
(0, max_z),
],
ring_markers=[
MINUS_Z_MARKER,
0,
PLUS_Z_MARKER
],
radial_subdiv=radial_subdiv,
)
inner_point_indices = tuple(range(len(inner_points)))
outer_points, outer_facets, outer_holes, outer_markers = \
generate_surface_of_revolution(
[(inner_r,min_z)] + rz + [(inner_r, max_z)],
ring_markers=[MINUS_Z_MARKER] + [0]*(len(rz)-1) + [PLUS_Z_MARKER],
point_idx_offset=len(inner_points),
radial_subdiv=radial_subdiv,
ring_point_indices=
[ inner_point_indices[:radial_subdiv] ]
+ [None]*len(rz)
+ [inner_point_indices[radial_subdiv:]]
)
mesh_info = MeshInfo()
mesh_info.set_points(inner_points + outer_points)
mesh_info.set_facets_ex(
inner_facets + outer_facets,
inner_holes + outer_holes,
inner_markers + outer_markers,
)
# set regional max. volume
mesh_info.regions.resize(2)
mesh_info.regions[0] = [0, 0, (max_z + min_z) / 2, 0, max_volume_inner]
mesh_info.regions[1] = [
inner_r + (rz[0][0] - inner_r) / 2, 0, (max_z + min_z) / 2, 0,
max_volume_outer
]
# add periodicity
mesh_info.pbc_groups.resize(1)
pbcg = mesh_info.pbc_groups[0]
pbcg.facet_marker_1 = MINUS_Z_MARKER
pbcg.facet_marker_2 = PLUS_Z_MARKER
pbcg.set_transform(translation=[0, 0, max_z - min_z])
mesh = build(mesh_info, verbose=True, volume_constraints=True)
#print "%d elements" % len(mesh.elements)
#mesh.write_vtk("gun.vtk")
fvi2fm = mesh.face_vertex_indices_to_face_marker
def zper_boundary_tagger(fvi, el, fn, points):
face_marker = fvi2fm[frozenset(fvi)]
if face_marker == MINUS_Z_MARKER:
return ["minus_z"]
elif face_marker == PLUS_Z_MARKER:
return ["plus_z"]
else:
return ["shell"]
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Tetrahedron
return make_conformal_mesh_ext(
vertices, [
Tetrahedron(i, el_idx, vertices)
for i, el_idx in enumerate(mesh.elements)
],
zper_boundary_tagger,
periodicity=[None, None, ("minus_z", "plus_z")])
def make_extrusion_with_fine_core(rz, inner_r,
max_volume_inner=1e-4, max_volume_outer=5e-2,
radial_subdiv=20):
min_z = min(rz_pt[1] for rz_pt in rz)
max_z = max(rz_pt[1] for rz_pt in rz)
from meshpy.tet import MeshInfo, build
from meshpy.geometry import generate_surface_of_revolution
MINUS_Z_MARKER = 1
PLUS_Z_MARKER = 2
inner_points, inner_facets, inner_holes, inner_markers = \
generate_surface_of_revolution(
[
(0, min_z),
(inner_r, min_z),
(inner_r, max_z),
(0, max_z),
],
ring_markers=[
MINUS_Z_MARKER,
0,
PLUS_Z_MARKER
],
radial_subdiv=radial_subdiv,
)
inner_point_indices = tuple(range(len(inner_points)))
outer_points, outer_facets, outer_holes, outer_markers = \
generate_surface_of_revolution(
[(inner_r,min_z)] + rz + [(inner_r, max_z)],
ring_markers=[MINUS_Z_MARKER] + [0]*(len(rz)-1) + [PLUS_Z_MARKER],
point_idx_offset=len(inner_points),
radial_subdiv=radial_subdiv,
ring_point_indices=
[ inner_point_indices[:radial_subdiv] ]
+ [None]*len(rz)
+ [inner_point_indices[radial_subdiv:]]
)
mesh_info = MeshInfo()
mesh_info.set_points(inner_points + outer_points)
mesh_info.set_facets_ex(
inner_facets + outer_facets,
inner_holes + outer_holes,
inner_markers + outer_markers,
)
# set regional max. volume
mesh_info.regions.resize(2)
mesh_info.regions[0] = [0, 0, (max_z+min_z)/2, 0,
max_volume_inner]
mesh_info.regions[1] = [inner_r+(rz[0][0]-inner_r)/2, 0, (max_z+min_z)/2, 0,
max_volume_outer]
# add periodicity
mesh_info.pbc_groups.resize(1)
pbcg = mesh_info.pbc_groups[0]
pbcg.facet_marker_1 = MINUS_Z_MARKER
pbcg.facet_marker_2 = PLUS_Z_MARKER
pbcg.set_transform(translation=[0,0,max_z-min_z])
mesh = build(mesh_info, verbose=True, volume_constraints=True)
#print "%d elements" % len(mesh.elements)
#mesh.write_vtk("gun.vtk")
fvi2fm = mesh.face_vertex_indices_to_face_marker
def zper_boundary_tagger(fvi, el, fn, points):
face_marker = fvi2fm[frozenset(fvi)]
if face_marker == MINUS_Z_MARKER:
return ["minus_z"]
elif face_marker == PLUS_Z_MARKER:
return ["plus_z"]
else:
return ["shell"]
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Tetrahedron
return make_conformal_mesh_ext(
vertices,
[Tetrahedron(i, el_idx, vertices)
for i, el_idx in enumerate(mesh.elements)],
zper_boundary_tagger,
periodicity=[None, None, ("minus_z", "plus_z")])
def build_mesh(self,
periodicity,
allow_internal_boundaries,
tag_mapper,
boundary_tagger=None):
# figure out dimensionalities
vol_dim = max(
el.el_type.dimensions
for key, el in self.gmsh_vertex_nrs_to_element.iteritems())
vol_elements = [
el for key, el in self.gmsh_vertex_nrs_to_element.iteritems()
if el.el_type.dimensions == vol_dim
]
# build hedge-compatible elements
from hedge.mesh.element import TO_CURVED_CLASS
hedge_vertices = []
hedge_elements = []
gmsh_node_nr_to_hedge_vertex_nr = {}
hedge_el_to_gmsh_element = {}
def get_vertex_nr(gmsh_node_nr):
try:
return gmsh_node_nr_to_hedge_vertex_nr[gmsh_node_nr]
except KeyError:
hedge_vertex_nr = len(hedge_vertices)
hedge_vertices.append(self.nodes[gmsh_node_nr])
gmsh_node_nr_to_hedge_vertex_nr[gmsh_node_nr] = hedge_vertex_nr
return hedge_vertex_nr
for el_nr, gmsh_el in enumerate(vol_elements):
el_map = LocalToGlobalMap(
[self.nodes[ni] for ni in gmsh_el.node_indices],
gmsh_el.el_type)
is_affine = el_map.is_affine()
el_class = gmsh_el.el_type.geometry
if not is_affine:
try:
el_class = TO_CURVED_CLASS[el_class]
except KeyError:
raise NotImplementedError(
"unsupported curved gmsh element type %s" % el_class)
vertex_indices = [
get_vertex_nr(gmsh_node_nr)
for gmsh_node_nr in gmsh_el.gmsh_vertex_indices
]
if is_affine:
hedge_el = el_class(el_nr, vertex_indices, hedge_vertices)
else:
hedge_el = el_class(el_nr, vertex_indices, el_map)
hedge_elements.append(hedge_el)
hedge_el_to_gmsh_element[hedge_el] = gmsh_el
from pytools import reverse_dictionary
hedge_vertex_nr_to_gmsh_node_nr = reverse_dictionary(
gmsh_node_nr_to_hedge_vertex_nr)
del vol_elements
def volume_tagger(el, all_v):
return [
self.tag_name_map[tag_nr, el.dimensions]
for tag_nr in hedge_el_to_gmsh_element[el].tag_numbers
if (tag_nr, el.dimensions) in self.tag_name_map
]
if boundary_tagger is None:
def boundary_tagger(fvi, el, fn, all_v):
gmsh_vertex_nrs = frozenset(
hedge_vertex_nr_to_gmsh_node_nr[face_vertex_index]
for face_vertex_index in fvi)
try:
gmsh_element = self.gmsh_vertex_nrs_to_element[
gmsh_vertex_nrs]
except KeyError:
return []
else:
x = [
self.tag_name_map[tag_nr, el.dimensions - 1]
for tag_nr in gmsh_element.tag_numbers
if (tag_nr, el.dimensions - 1) in self.tag_name_map
]
if len(x) > 1:
from pudb import set_trace
set_trace()
return x
vertex_array = np.array(hedge_vertices, dtype=np.float64)
pt_dim = vertex_array.shape[-1]
if pt_dim != vol_dim:
from warnings import warn
warn("Found %d-dimensional mesh embedded in %d-dimensional space. "
"Hedge only supports meshes of zero codimension (for now). "
"Maybe you want to set force_dimension=%d?" %
(vol_dim, pt_dim, vol_dim))
from hedge.mesh import make_conformal_mesh_ext
return make_conformal_mesh_ext(
vertex_array,
hedge_elements,
boundary_tagger=boundary_tagger,
volume_tagger=volume_tagger,
periodicity=periodicity,
allow_internal_boundaries=allow_internal_boundaries)
def build_mesh(self):
# figure out dimensionalities
node_dim = single_valued(len(node) for node in nodes)
vol_dim = max(el.el_type.dimensions for key, el in gmsh_vertex_nrs_to_element.iteritems())
bdry_dim = vol_dim - 1
vol_elements = [el for key, el in gmsh_vertex_nrs_to_element.iteritems() if el.el_type.dimensions == vol_dim]
bdry_elements = [el for key, el in gmsh_vertex_nrs_to_element.iteritems() if el.el_type.dimensions == bdry_dim]
# build hedge-compatible elements
from hedge.mesh.element import TO_CURVED_CLASS
hedge_vertices = []
hedge_elements = []
gmsh_node_nr_to_hedge_vertex_nr = {}
hedge_el_to_gmsh_element = {}
def get_vertex_nr(gmsh_node_nr):
try:
return gmsh_node_nr_to_hedge_vertex_nr[gmsh_node_nr]
except KeyError:
hedge_vertex_nr = len(hedge_vertices)
hedge_vertices.append(nodes[gmsh_node_nr])
gmsh_node_nr_to_hedge_vertex_nr[gmsh_node_nr] = hedge_vertex_nr
return hedge_vertex_nr
for el_nr, gmsh_el in enumerate(vol_elements):
el_map = LocalToGlobalMap([nodes[ni] for ni in gmsh_el.node_indices], gmsh_el.el_type)
is_affine = el_map.is_affine()
el_class = gmsh_el.el_type.geometry
if not is_affine:
try:
el_class = TO_CURVED_CLASS[el_class]
except KeyError:
raise GmshFileFormatError("unsupported curved element type %s" % el_class)
vertex_indices = [get_vertex_nr(gmsh_node_nr) for gmsh_node_nr in gmsh_el.gmsh_vertex_indices]
if is_affine:
hedge_el = el_class(el_nr, vertex_indices, hedge_vertices)
else:
hedge_el = el_class(el_nr, vertex_indices, el_map)
hedge_elements.append(hedge_el)
hedge_el_to_gmsh_element[hedge_el] = gmsh_el
from pytools import reverse_dictionary
hedge_vertex_nr_to_gmsh_node_nr = reverse_dictionary(gmsh_node_nr_to_hedge_vertex_nr)
del vol_elements
def volume_tagger(el, all_v):
return [
tag_name_map[tag_nr, el.dimensions]
for tag_nr in hedge_el_to_gmsh_element[el].tag_numbers
if (tag_nr, el.dimensions) in tag_name_map
]
def boundary_tagger(fvi, el, fn, all_v):
gmsh_vertex_nrs = frozenset(hedge_vertex_nr_to_gmsh_node_nr[face_vertex_index] for face_vertex_index in fvi)
try:
gmsh_element = gmsh_vertex_nrs_to_element[gmsh_vertex_nrs]
except KeyError:
return []
else:
x = [
tag_name_map[tag_nr, el.dimensions - 1]
for tag_nr in gmsh_element.tag_numbers
if (tag_nr, el.dimensions - 1) in tag_name_map
]
if len(x) > 1:
from pudb import set_trace
set_trace()
return x
vertex_array = np.array(hedge_vertices, dtype=np.float64)
pt_dim = vertex_array.shape[-1]
if pt_dim != vol_dim:
from warnings import warn
warn(
"Found %d-dimensional mesh embedded in %d-dimensional space. "
"Hedge only supports meshes of zero codimension (for now). "
"Maybe you want to set force_dimension=%d?" % (vol_dim, pt_dim, vol_dim)
)
from hedge.mesh import make_conformal_mesh_ext
return make_conformal_mesh_ext(
vertex_array,
hedge_elements,
boundary_tagger=boundary_tagger,
volume_tagger=volume_tagger,
periodicity=periodicity,
allow_internal_boundaries=allow_internal_boundaries,
)
def make_squaremesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i+1)%len(seq)))
return result
def needs_refinement(vertices, area):
x = sum(numpy.array(v) for v in vertices)/3
max_area_volume = 0.7e-2 + 0.03*(0.05*x[1]**2 + 0.3*min(x[0]+1,0)**2)
max_area_corners = 1e-3 + 0.001*max(
la.norm(x-corner)**4 for corner in obstacle_corners)
return bool(area > 2.5*min(max_area_volume, max_area_corners))
from meshpy.geometry import make_box
points, facets, _, _ = make_box((-0.5,-0.5), (0.5,0.5))
obstacle_corners = points[:]
from meshpy.geometry import GeometryBuilder, Marker
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points, facets=facets,
facet_markers=profile_marker)
points, facets, _, facet_markers = make_box((-16, -22), (25, 22))
builder.add_geometry(points=points, facets=facets,
facet_markers=facet_markers)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([(0,0)])
mesh = build(mi, refinement_func=needs_refinement,
allow_boundary_steiner=True,
generate_faces=True)
print "%d elements" % len(mesh.elements)
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mesh)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(mesh.elements)],
bdry_tagger)
def make_nacamesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
pt_back = numpy.array([1, 0])
# def max_area(pt):
# max_area_front = 1e-2*la.norm(pt)**2 + 1e-5
# max_area_back = 1e-2*la.norm(pt-pt_back)**2 + 1e-4
# return min(max_area_front, max_area_back)
def max_area(pt):
x = pt[0]
if x < 0:
return 1e-2 * la.norm(pt) ** 2 + 1e-5
elif x > 1:
return 1e-2 * la.norm(pt - pt_back) ** 2 + 1e-5
else:
return 1e-2 * pt[1] ** 2 + 1e-5
def needs_refinement(vertices, area):
barycenter = sum(numpy.array(v) for v in vertices) / 3
return bool(area > max_area(barycenter))
from meshpy.naca import get_naca_points
points = get_naca_points(naca_digits="2412", number_of_points=80)
from meshpy.geometry import GeometryBuilder, Marker
from meshpy.triangle import write_gnuplot_mesh
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points, facets=round_trip_connect(points), facet_markers=profile_marker)
builder.wrap_in_box(4, (10, 8))
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([builder.center()])
mesh = build(
mi,
refinement_func=needs_refinement,
# allow_boundary_steiner=False,
generate_faces=True,
)
write_gnuplot_mesh("mesh.dat", mesh)
print "%d elements" % len(mesh.elements)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
# Marker.MINUS_Y: "minus_y",
# Marker.PLUS_Y: "plus_y"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, order="C")
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices) for i, el_idx in enumerate(mesh.elements)],
bdry_tagger,
# periodicity=[None, ("minus_y", "plus_y")]
)
def parse_gmsh(line_iterable, force_dimension=None, periodicity=None,
allow_internal_boundaries=False, tag_mapper=lambda tag: tag):
"""
:param force_dimension: if not None, truncate point coordinates to this many dimensions.
"""
feeder = LineFeeder(line_iterable)
element_type_map = GMSH_ELEMENT_TYPE_TO_INFO_MAP
# collect the mesh information
nodes = []
elements = []
# maps (tag_number, dimension) -> tag_name
tag_name_map = {}
gmsh_vertex_nrs_to_element = {}
class ElementInfo(Record):
pass
while feeder.has_next_line():
next_line = feeder.get_next_line()
if not next_line.startswith("$"):
raise GmshFileFormatError("expected start of section, '%s' found instead" % next_line)
section_name = next_line[1:]
if section_name == "MeshFormat":
line_count = 0
while True:
next_line = feeder.get_next_line()
if next_line == "$End"+section_name:
break
if line_count == 0:
version_number, file_type, data_size = next_line.split()
if line_count > 0:
raise GmshFileFormatError("more than one line found in MeshFormat section")
if version_number not in ["2.1", "2.2"]:
from warnings import warn
warn("unexpected mesh version number '%s' found" % version_number)
if file_type != "0":
raise GmshFileFormatError("only ASCII gmsh file type is supported")
line_count += 1
elif section_name == "Nodes":
node_count = int(feeder.get_next_line())
node_idx = 1
while True:
next_line = feeder.get_next_line()
if next_line == "$End"+section_name:
break
parts = next_line.split()
if len(parts) != 4:
raise GmshFileFormatError("expected four-component line in $Nodes section")
read_node_idx = int(parts[0])
if read_node_idx != node_idx:
raise GmshFileFormatError("out-of-order node index found")
if force_dimension is not None:
point = [float(x) for x in parts[1:force_dimension+1]]
else:
point = [float(x) for x in parts[1:]]
nodes.append(numpy.array(point, dtype=numpy.float64))
node_idx += 1
if node_count+1 != node_idx:
raise GmshFileFormatError("unexpected number of nodes found")
elif section_name == "Elements":
element_count = int(feeder.get_next_line())
element_idx = 1
while True:
next_line = feeder.get_next_line()
if next_line == "$End"+section_name:
break
parts = [int(x) for x in next_line.split()]
if len(parts) < 4:
raise GmshFileFormatError("too few entries in element line")
read_element_idx = parts[0]
if read_element_idx != element_idx:
raise GmshFileFormatError("out-of-order node index found")
el_type_num = parts[1]
try:
element_type = element_type_map[el_type_num]
except KeyError:
raise GmshFileFormatError("unexpected element type %d"
% el_type_num)
tag_count = parts[2]
tags = parts[3:3+tag_count]
# convert to zero-based
node_indices = [x-1 for x in parts[3+tag_count:]]
if element_type.node_count()!= len(node_indices):
raise GmshFileFormatError("unexpected number of nodes in element")
gmsh_vertex_nrs = node_indices[:element_type.vertex_count]
zero_based_idx = element_idx - 1
el_info = ElementInfo(
index=zero_based_idx,
el_type=element_type,
node_indices=node_indices,
gmsh_vertex_indices=gmsh_vertex_nrs,
tag_numbers=[tag for tag in tags[:1] if tag != 0])
gmsh_vertex_nrs_to_element[frozenset(gmsh_vertex_nrs)] = el_info
element_idx +=1
if element_count+1 != element_idx:
raise GmshFileFormatError("unexpected number of elements found")
elif section_name == "PhysicalNames":
name_count = int(feeder.get_next_line())
name_idx = 1
while True:
next_line = feeder.get_next_line()
if next_line == "$End"+section_name:
break
dimension, number, name = next_line.split(" ", 2)
dimension = int(dimension)
number = int(number)
if not name[0] == '"' or not name[-1] == '"':
raise GmshFileFormatError("expected quotes around physical name")
tag_name_map[number, dimension] = tag_mapper(name[1:-1])
name_idx +=1
if name_count+1 != name_idx:
raise GmshFileFormatError("unexpected number of physical names found")
else:
# unrecognized section, skip
while True:
next_line = feeder.get_next_line()
if next_line == "$End"+section_name:
break
# figure out dimensionalities
node_dim = single_valued(len(node) for node in nodes)
vol_dim = max(el.el_type.dimensions for key, el in
gmsh_vertex_nrs_to_element.iteritems() )
bdry_dim = vol_dim - 1
vol_elements = [el for key, el in gmsh_vertex_nrs_to_element.iteritems()
if el.el_type.dimensions == vol_dim]
bdry_elements = [el for key, el in gmsh_vertex_nrs_to_element.iteritems()
if el.el_type.dimensions == bdry_dim]
# build hedge-compatible elements
from hedge.mesh.element import TO_CURVED_CLASS
hedge_vertices = []
hedge_elements = []
gmsh_node_nr_to_hedge_vertex_nr = {}
hedge_el_to_gmsh_element = {}
def get_vertex_nr(gmsh_node_nr):
try:
return gmsh_node_nr_to_hedge_vertex_nr[gmsh_node_nr]
except KeyError:
hedge_vertex_nr = len(hedge_vertices)
hedge_vertices.append(nodes[gmsh_node_nr])
gmsh_node_nr_to_hedge_vertex_nr[gmsh_node_nr] = hedge_vertex_nr
return hedge_vertex_nr
for el_nr, gmsh_el in enumerate(vol_elements):
el_map = LocalToGlobalMap(
[nodes[ni] for ni in gmsh_el.node_indices],
gmsh_el.el_type)
is_affine = el_map.is_affine()
el_class = gmsh_el.el_type.geometry
if not is_affine:
try:
el_class = TO_CURVED_CLASS[el_class]
except KeyError:
raise GmshFileFormatError("unsupported curved element type %s" % el_class)
vertex_indices = [get_vertex_nr(gmsh_node_nr)
for gmsh_node_nr in gmsh_el.gmsh_vertex_indices]
if is_affine:
hedge_el = el_class(el_nr, vertex_indices, hedge_vertices)
else:
hedge_el = el_class(el_nr, vertex_indices, el_map)
hedge_elements.append(hedge_el)
hedge_el_to_gmsh_element[hedge_el] = gmsh_el
from pytools import reverse_dictionary
hedge_vertex_nr_to_gmsh_node_nr = reverse_dictionary(
gmsh_node_nr_to_hedge_vertex_nr)
del vol_elements
def volume_tagger(el, all_v):
return [tag_name_map[tag_nr, el.dimensions]
for tag_nr in hedge_el_to_gmsh_element[el].tag_numbers
if (tag_nr, el.dimensions) in tag_name_map]
def boundary_tagger(fvi, el, fn, all_v):
gmsh_vertex_nrs = frozenset(
hedge_vertex_nr_to_gmsh_node_nr[face_vertex_index]
for face_vertex_index in fvi)
try:
gmsh_element = gmsh_vertex_nrs_to_element[gmsh_vertex_nrs]
except KeyError:
return []
else:
x = [tag_name_map[tag_nr, el.dimensions-1]
for tag_nr in gmsh_element.tag_numbers
if (tag_nr, el.dimensions-1) in tag_name_map]
if len(x) > 1:
from pudb import set_trace; set_trace()
return x
vertex_array = numpy.array(hedge_vertices, dtype=numpy.float64)
pt_dim = vertex_array.shape[-1]
if pt_dim != vol_dim:
from warnings import warn
warn("Found %d-dimensional mesh embedded in %d-dimensional space. "
"Hedge only supports meshes of zero codimension (for now). "
"Maybe you want to set force_dimension=%d?"
% (vol_dim, pt_dim, vol_dim))
from hedge.mesh import make_conformal_mesh_ext
return make_conformal_mesh_ext(
vertex_array,
hedge_elements,
boundary_tagger=boundary_tagger,
volume_tagger=volume_tagger,
periodicity=periodicity,
allow_internal_boundaries=allow_internal_boundaries)
def make_box_mesh(a=(0, 0, 0), b=(1, 1, 1),
max_volume=None, periodicity=None,
boundary_tagger=(lambda fvi, el, fn, all_v: []),
return_meshpy_mesh=False):
"""Return a mesh for a brick from the origin to `dimensions`.
*max_volume* specifies the maximum volume for each tetrahedron.
*periodicity* is either None, or a triple of bools, indicating
whether periodic BCs are to be applied along that axis.
See :func:`make_conformal_mesh` for the meaning of *boundary_tagger*.
A few stock boundary tags are provided for easy application
of boundary conditions, namely plus_[xyz] and minus_[xyz] tag
the appropriate faces of the brick.
"""
def count(iterable):
result = 0
for i in iterable:
result += 1
return result
from meshpy.tet import MeshInfo, build
from meshpy.geometry import make_box
points, facets, _, facet_markers = make_box(a, b)
mesh_info = MeshInfo()
mesh_info.set_points(points)
mesh_info.set_facets(facets, facet_markers)
if periodicity is None:
periodicity = (False, False, False)
axes = ["x", "y", "z"]
per_count = count(p for p in periodicity if p)
marker_to_tag = {}
mesh_periodicity = []
periodic_tags = set()
if per_count:
mesh_info.pbc_groups.resize(per_count)
pbc_group_number = 0
for axis, axis_per in enumerate(periodicity):
minus_marker = 1+2*axis
plus_marker = 2+2*axis
minus_tag = "minus_"+axes[axis]
plus_tag = "plus_"+axes[axis]
marker_to_tag[minus_marker] = minus_tag
marker_to_tag[plus_marker] = plus_tag
if axis_per:
pbcg = mesh_info.pbc_groups[pbc_group_number]
pbc_group_number += 1
pbcg.facet_marker_1 = minus_marker
pbcg.facet_marker_2 = plus_marker
translation = [0, 0, 0]
translation[axis] = b[axis]-a[axis]
pbcg.set_transform(translation=translation)
mesh_periodicity.append((minus_tag, plus_tag))
periodic_tags.add(minus_tag)
periodic_tags.add(plus_tag)
else:
mesh_periodicity.append(None)
generated_mesh = build(mesh_info, max_volume=max_volume)
fvi2fm = generated_mesh.face_vertex_indices_to_face_marker
def wrapped_boundary_tagger(fvi, el, fn, all_v):
face_tag = marker_to_tag[fvi2fm[frozenset(fvi)]]
if face_tag in periodic_tags:
return [face_tag]
else:
return [face_tag] + boundary_tagger(fvi, el, fn, all_v)
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Tetrahedron
vertices = numpy.asarray(generated_mesh.points, dtype=float, order="C")
result = make_conformal_mesh_ext(
vertices,
[Tetrahedron(i, el_idx, vertices)
for i, el_idx in enumerate(generated_mesh.elements)],
wrapped_boundary_tagger,
periodicity=mesh_periodicity)
if return_meshpy_mesh:
return result, generated_mesh
else:
return result
def make_centered_regular_rect_mesh(a=(0, 0), b=(1, 1), n=(5, 5), periodicity=None,
post_refine_factor=1, boundary_tagger=(lambda fvi, el, fn, all_v: [])):
"""Create a semi-structured rectangular mesh.
:param a: the lower left hand point of the rectangle
:param b: the upper right hand point of the rectangle
:param n: a tuple of integers indicating the total number of points
on [a,b].
:param periodicity: either None, or a tuple of bools specifying whether
the mesh is to be periodic in x and y.
"""
if min(n) < 2:
raise ValueError("need at least two points in each direction")
node_dict = {}
centered_node_dict = {}
points = []
points_1d = [numpy.linspace(a_i, b_i, n_i)
for a_i, b_i, n_i in zip(a, b, n)]
dx = (numpy.array(b, dtype=numpy.float64)
- numpy.array(a, dtype=numpy.float64)) / (numpy.array(n)-1)
half_dx = dx/2
for j in range(n[1]):
for i in range(n[0]):
node_dict[i, j] = len(points)
points.append(numpy.array([points_1d[0][i], points_1d[1][j]]))
for j in range(n[1]-1):
for i in range(n[0]-1):
centered_node_dict[i, j] = len(points)
points.append(numpy.array([points_1d[0][i], points_1d[1][j]]) + half_dx)
elements = []
if periodicity is None:
periodicity = (False, False)
axes = ["x", "y"]
mesh_periodicity = []
periodic_tags = set()
for i, axis in enumerate(axes):
if periodicity[i]:
minus_tag = "minus_"+axis
plus_tag = "plus_"+axis
mesh_periodicity.append((minus_tag, plus_tag))
periodic_tags.add(minus_tag)
periodic_tags.add(plus_tag)
else:
mesh_periodicity.append(None)
fvi2fm = {}
for i in range(n[0]-1):
for j in range(n[1]-1):
# c---d
# |\ /|
# | m |
# |/ \|
# a---b
a = node_dict[i, j]
b = node_dict[i+1, j]
c = node_dict[i, j+1]
d = node_dict[i+1, j+1]
m = centered_node_dict[i, j]
elements.append((a, b, m))
elements.append((b, d, m))
elements.append((d, c, m))
elements.append((c, a, m))
if i == 0:
fvi2fm[frozenset((a, c))] = "minus_x"
if i == n[0]-2:
fvi2fm[frozenset((b, d))] = "plus_x"
if j == 0:
fvi2fm[frozenset((a, b))] = "minus_y"
if j == n[1]-2:
fvi2fm[frozenset((c, d))] = "plus_y"
def wrapped_boundary_tagger(fvi, el, fn, all_v):
btag = fvi2fm[frozenset(fvi)]
if btag in periodic_tags:
return [btag]
else:
return [btag] + boundary_tagger(fvi, el, fn, all_v)
if post_refine_factor > 1:
from meshpy.tools import uniform_refine_triangles
points, elements, of2nf = uniform_refine_triangles(
points, elements, post_refine_factor)
old_fvi2fm = fvi2fm
fvi2fm = {}
for fvi, fm in old_fvi2fm.iteritems():
for new_fvi in of2nf[fvi]:
fvi2fm[frozenset(new_fvi)] = fm
vertices = numpy.asarray(points, dtype=float, order="C")
from hedge.mesh import make_conformal_mesh_ext
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(
vertices,
[Triangle(i, el_idx, vertices)
for i, el_idx in enumerate(elements)],
wrapped_boundary_tagger,
periodicity=mesh_periodicity)
def make_squaremesh():
def round_trip_connect(seq):
result = []
for i in range(len(seq)):
result.append((i, (i + 1) % len(seq)))
return result
def needs_refinement(vertices, area):
x = sum(numpy.array(v) for v in vertices) / 3
max_area_volume = 0.7e-2 + 0.03 * (0.05 * x[1]**2 +
0.3 * min(x[0] + 1, 0)**2)
max_area_corners = 1e-3 + 0.001 * max(
la.norm(x - corner)**4 for corner in obstacle_corners)
return bool(area > 2.5 * min(max_area_volume, max_area_corners))
from meshpy.geometry import make_box
points, facets, _, _ = make_box((-0.5, -0.5), (0.5, 0.5))
obstacle_corners = points[:]
from meshpy.geometry import GeometryBuilder, Marker
profile_marker = Marker.FIRST_USER_MARKER
builder = GeometryBuilder()
builder.add_geometry(points=points,
facets=facets,
facet_markers=profile_marker)
points, facets, _, facet_markers = make_box((-16, -22), (25, 22))
builder.add_geometry(points=points,
facets=facets,
facet_markers=facet_markers)
from meshpy.triangle import MeshInfo, build
mi = MeshInfo()
builder.set(mi)
mi.set_holes([(0, 0)])
mesh = build(mi,
refinement_func=needs_refinement,
allow_boundary_steiner=True,
generate_faces=True)
print "%d elements" % len(mesh.elements)
from meshpy.triangle import write_gnuplot_mesh
write_gnuplot_mesh("mesh.dat", mesh)
fvi2fm = mesh.face_vertex_indices_to_face_marker
face_marker_to_tag = {
profile_marker: "noslip",
Marker.MINUS_X: "inflow",
Marker.PLUS_X: "outflow",
Marker.MINUS_Y: "inflow",
Marker.PLUS_Y: "inflow"
}
def bdry_tagger(fvi, el, fn, all_v):
face_marker = fvi2fm[fvi]
return [face_marker_to_tag[face_marker]]
from hedge.mesh import make_conformal_mesh_ext
vertices = numpy.asarray(mesh.points, dtype=float, order="C")
from hedge.mesh.element import Triangle
return make_conformal_mesh_ext(vertices, [
Triangle(i, el_idx, vertices) for i, el_idx in enumerate(mesh.elements)
], bdry_tagger)