import numpy as np
import ufl
from pyop2.mpi import COMM_WORLD
from firedrake.utils import IntType, ScalarType
from firedrake import (
VectorFunctionSpace,
FunctionSpace,
Function,
Constant,
assemble,
Interpolate,
FiniteElement,
interval,
tetrahedron,
atan2,
pi,
as_vector,
SpatialCoordinate,
conditional,
gt,
as_tensor,
dot,
And,
Or,
sin,
cos,
real
)
from firedrake.cython import dmcommon
from firedrake import mesh
from firedrake import function
from firedrake import functionspace
from firedrake.petsc import PETSc
from pyadjoint.tape import no_annotations
__all__ = [
"IntervalMesh",
"UnitIntervalMesh",
"PeriodicIntervalMesh",
"PeriodicUnitIntervalMesh",
"UnitTriangleMesh",
"RectangleMesh",
"TensorRectangleMesh",
"SquareMesh",
"UnitSquareMesh",
"PeriodicRectangleMesh",
"PeriodicSquareMesh",
"PeriodicUnitSquareMesh",
"CircleManifoldMesh",
"UnitDiskMesh",
"UnitBallMesh",
"UnitTetrahedronMesh",
"TensorBoxMesh",
"BoxMesh",
"CubeMesh",
"UnitCubeMesh",
"PeriodicBoxMesh",
"PeriodicUnitCubeMesh",
"IcosahedralSphereMesh",
"UnitIcosahedralSphereMesh",
"OctahedralSphereMesh",
"UnitOctahedralSphereMesh",
"CubedSphereMesh",
"UnitCubedSphereMesh",
"TorusMesh",
"AnnulusMesh",
"SolidTorusMesh",
"CylinderMesh",
]
distribution_parameters_no_overlap = {"partition": True,
"overlap_type": (mesh.DistributedMeshOverlapType.NONE, 0)}
reorder_noop = False
def _postprocess_periodic_mesh(coords, comm, distribution_parameters, reorder, name, distribution_name, permutation_name):
dm = coords.function_space().mesh().topology.topology_dm
dm.removeLabel("pyop2_core")
dm.removeLabel("pyop2_owned")
dm.removeLabel("pyop2_ghost")
dm.removeLabel("exterior_facets")
dm.removeLabel("interior_facets")
V = coords.function_space()
dmcommon._set_dg_coordinates(dm,
V.finat_element,
V.dm.getLocalSection(),
coords.dat._vec)
return mesh.Mesh(
dm,
comm=comm,
distribution_parameters=distribution_parameters,
reorder=reorder,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def IntervalMesh(
ncells,
length_or_left,
right=None,
distribution_parameters=None,
reorder=False,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""
Generate a uniform mesh of an interval.
:arg ncells: The number of the cells over the interval.
:arg length_or_left: The length of the interval (if ``right``
is not provided) or else the left hand boundary point.
:arg right: (optional) position of the right
boundary point (in which case ``length_or_left`` should
be the left boundary point).
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The left hand boundary point has boundary marker 1,
while the right hand point has marker 2.
"""
if right is None:
left = 0
right = length_or_left
else:
left = length_or_left
if ncells <= 0 or ncells % 1:
raise ValueError("Number of cells must be a postive integer")
length = right - left
if length < 0:
raise ValueError("Requested mesh has negative length")
dx = length / ncells
# This ensures the rightmost point is actually present.
coords = np.arange(left, right + 0.01 * dx, dx, dtype=np.double).reshape(-1, 1)
cells = np.dstack(
(
np.arange(0, len(coords) - 1, dtype=np.int32),
np.arange(1, len(coords), dtype=np.int32),
)
).reshape(-1, 2)
plex = mesh.plex_from_cell_list(
1, cells, coords, comm, mesh._generate_default_mesh_topology_name(name)
)
# Apply boundary IDs
plex.createLabel(dmcommon.FACE_SETS_LABEL)
coordinates = plex.getCoordinates()
coord_sec = plex.getCoordinateSection()
vStart, vEnd = plex.getDepthStratum(0) # vertices
for v in range(vStart, vEnd):
vcoord = plex.vecGetClosure(coord_sec, coordinates, v)
if vcoord[0] == coords[0]:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, v, 1)
if vcoord[0] == coords[-1]:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, v, 2)
m = mesh.Mesh(
plex,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
[docs]
@PETSc.Log.EventDecorator()
def UnitIntervalMesh(
ncells,
distribution_parameters=None,
reorder=False,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""
Generate a uniform mesh of the interval [0,1].
:arg ncells: The number of the cells over the interval.
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The left hand (:math:`x=0`) boundary point has boundary marker 1,
while the right hand (:math:`x=1`) point has marker 2.
"""
return IntervalMesh(
ncells,
length_or_left=1.0,
distribution_parameters=distribution_parameters,
reorder=reorder,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def PeriodicIntervalMesh(
ncells,
length,
distribution_parameters=None,
reorder=False,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a periodic mesh of an interval.
:arg ncells: The number of cells over the interval.
:arg length: The length the interval.
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
if ncells < 3:
raise ValueError(
"1D periodic meshes with fewer than 3 \
cells are not currently supported"
)
m = CircleManifoldMesh(
ncells,
distribution_parameters=distribution_parameters_no_overlap,
reorder=reorder_noop,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
indicator = Function(FunctionSpace(m, "DG", 0))
coord_fs = VectorFunctionSpace(
m, FiniteElement("DG", interval, 1, variant="equispaced"), dim=1
)
new_coordinates = Function(
coord_fs, name=mesh._generate_default_mesh_coordinates_name(name)
)
x, y = SpatialCoordinate(m)
eps = 1.e-14
indicator.interpolate(conditional(gt(real(y), 0), 0., 1.))
new_coordinates.interpolate(
as_vector((conditional(
gt(real(x), real(1. - eps)), indicator, # Periodic break.
# Unwrap rest of circle.
atan2(real(-y), real(-x))/(2 * pi) + 0.5
) * length,))
)
return _postprocess_periodic_mesh(new_coordinates,
comm,
distribution_parameters,
reorder,
name,
distribution_name,
permutation_name)
[docs]
@PETSc.Log.EventDecorator()
def PeriodicUnitIntervalMesh(
ncells,
distribution_parameters=None,
reorder=False,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a periodic mesh of the unit interval.
:arg ncells: The number of cells in the interval.
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
return PeriodicIntervalMesh(
ncells,
length=1.0,
distribution_parameters=distribution_parameters,
reorder=reorder,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
@PETSc.Log.EventDecorator()
def OneElementThickMesh(
ncells,
Lx,
Ly,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""
Generate a rectangular mesh in the domain with corners [0,0]
and [Lx, Ly] with ncells, that is periodic in the x-direction.
:arg ncells: The number of cells in the mesh.
:arg Lx: The width of the domain in the x-direction.
:arg Ly: The width of the domain in the y-direction.
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
left = np.arange(ncells, dtype=np.int32)
right = np.roll(left, -1)
cells = np.array([left, left, right, right]).T
dx = Lx / ncells
X = np.arange(1.0 * ncells, dtype=np.double) * dx
Y = 0.0 * X
coords = np.array([X, Y]).T
# a line of coordinates, with a looped topology
plex = mesh.plex_from_cell_list(
2, cells, coords, comm, mesh._generate_default_mesh_topology_name(name)
)
mesh1 = mesh.Mesh(plex, distribution_parameters=distribution_parameters, comm=comm)
mesh1.topology.init()
cell_numbering = mesh1._cell_numbering
cell_range = plex.getHeightStratum(0)
cell_closure = np.zeros((cell_range[1], 9), dtype=IntType)
# Get the coordinates for this process
coords = plex.getCoordinatesLocal().array_r
# get the PETSc section
coords_sec = plex.getCoordinateSection()
for e in range(*cell_range):
closure, _ = plex.getTransitiveClosure(e)
# get the row for this cell
row = cell_numbering.getOffset(e)
# run some checks
assert closure[0] == e
assert len(closure) == 6, closure
edge_range = plex.getHeightStratum(1)
assert all(closure[1:4] >= edge_range[0])
assert all(closure[1:4] < edge_range[1])
vertex_range = plex.getHeightStratum(2)
assert all(closure[4:] >= vertex_range[0])
assert all(closure[4:] < vertex_range[1])
# enter the cell number
cell_closure[row][8] = e
# Get a list of unique edges
edge_set = list(closure[1:4])
# there are two vertices in the cell
cell_vertices = closure[4:]
cell_X = np.array([0.0, 0.0], dtype=ScalarType)
for i, v in enumerate(cell_vertices):
cell_X[i] = coords[coords_sec.getOffset(v)]
# Add in the edges
for i in range(3):
edge_vertex, edge_vertex_ = plex.getCone(edge_set[i])
if edge_vertex_ != edge_vertex:
# we have a y-periodic edge
cell_closure[row][6] = edge_set[i]
cell_closure[row][7] = edge_set[i]
else:
# in this code we check if it is a right edge, or a left edge
# by inspecting the x coordinates of the edge vertex (1)
# and comparing with the x coordinates of the cell vertices (2)
# there is only one vertex on the edge in this case
# get X coordinate for this edge
edge_X = coords[coords_sec.getOffset(edge_vertex)]
# get X coordinates for this cell
if cell_X.min() < dx / 2:
if cell_X.max() < 3 * dx / 2:
# We are in the first cell
if edge_X.min() < dx / 2:
# we are on left hand edge
cell_closure[row][4] = edge_set[i]
else:
# we are on right hand edge
cell_closure[row][5] = edge_set[i]
else:
# We are in the last cell
if edge_X.min() < dx / 2:
# we are on right hand edge
cell_closure[row][5] = edge_set[i]
else:
# we are on left hand edge
cell_closure[row][4] = edge_set[i]
else:
if abs(cell_X.min() - edge_X.min()) < dx / 2:
# we are on left hand edge
cell_closure[row][4] = edge_set[i]
else:
# we are on right hand edge
cell_closure[row][5] = edge_set[i]
# Add in the vertices
vertices = closure[4:]
v1 = vertices[0]
v2 = vertices[1]
x1 = coords[coords_sec.getOffset(v1)]
x2 = coords[coords_sec.getOffset(v2)]
# Fix orientations
if x1 > x2:
if x1 - x2 < dx * 1.5:
# we are not on the rightmost cell and need to swap
v1, v2 = v2, v1
elif x2 - x1 > dx * 1.5:
# we are on the rightmost cell and need to swap
v1, v2 = v2, v1
cell_closure[row][0:4] = [v1, v1, v2, v2]
mesh1.topology.cell_closure = np.array(cell_closure, dtype=IntType)
mesh1.init()
fe_dg = FiniteElement("DQ", mesh1.ufl_cell(), 1, variant="equispaced")
Vc = VectorFunctionSpace(mesh1, fe_dg)
fc = Function(
Vc, name=mesh._generate_default_mesh_coordinates_name(name)
).interpolate(mesh1.coordinates)
mash = mesh.Mesh(
fc,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
topverts = Vc.cell_node_list[:, 1::2].flatten()
mash.coordinates.dat.data_with_halos[topverts, 1] = Ly
# search for the last cell
mcoords_ro = mash.coordinates.dat.data_ro_with_halos
mcoords = mash.coordinates.dat.data_with_halos
for e in range(*cell_range):
cell = cell_numbering.getOffset(e)
cell_nodes = Vc.cell_node_list[cell, :]
Xvals = mcoords_ro[cell_nodes, 0]
if Xvals.max() - Xvals.min() > Lx / 2:
mcoords[cell_nodes[2:], 0] = Lx
else:
mcoords
local_facet_dat = mash.topology.interior_facets.local_facet_dat
lfd = local_facet_dat.data
for i in range(lfd.shape[0]):
if all(lfd[i, :] == np.array([3, 3])):
lfd[i, :] = [2, 3]
return mash
[docs]
@PETSc.Log.EventDecorator()
def UnitTriangleMesh(
refinement_level=0,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of the reference triangle
:kwarg refinement_level: Number of uniform refinements to perform
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
coords = [[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]]
cells = [[0, 1, 2]]
plex = mesh.plex_from_cell_list(2, cells, coords, comm)
# mark boundary facets
plex.createLabel(dmcommon.FACE_SETS_LABEL)
plex.markBoundaryFaces("boundary_faces")
coords = plex.getCoordinates()
coord_sec = plex.getCoordinateSection()
boundary_faces = plex.getStratumIS("boundary_faces", 1).getIndices()
tol = 1e-2 # 0.5 would suffice
for face in boundary_faces:
face_coords = plex.vecGetClosure(coord_sec, coords, face)
# |x+y-1| < eps
if abs(face_coords[0] + face_coords[1] - 1) < tol and abs(face_coords[2] + face_coords[3] - 1) < tol:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 1)
# |x| < eps
if abs(face_coords[0]) < tol and abs(face_coords[2]) < tol:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 2)
# |y| < eps
if abs(face_coords[1]) < tol and abs(face_coords[3]) < tol:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 3)
plex.removeLabel("boundary_faces")
plex.setRefinementUniform(True)
for i in range(refinement_level):
plex = plex.refine()
plex.setName(mesh._generate_default_mesh_topology_name(name))
return mesh.Mesh(
plex,
reorder=False,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
[docs]
@PETSc.Log.EventDecorator()
def RectangleMesh(
nx,
ny,
Lx,
Ly,
originX=0.,
originY=0.,
quadrilateral=False,
reorder=None,
diagonal="left",
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a rectangular mesh
:arg nx: The number of cells in the x direction.
:arg ny: The number of cells in the y direction.
:arg Lx: The X coordinates of the upper right corner of the rectangle.
:arg Ly: The Y coordinates of the upper right corner of the rectangle.
:arg originX: The X coordinates of the lower left corner of the rectangle.
:arg originY: The Y coordinates of the lower left corner of the rectangle.
:kwarg quadrilateral: (optional), creates quadrilateral mesh, defaults to False
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg diagonal: For triangular meshes, should the diagonal got
from bottom left to top right (``"right"``), or top left to
bottom right (``"left"``), or put in both diagonals (``"crossed"``).
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The boundary edges in this mesh are numbered as follows:
* 1: plane x == originX
* 2: plane x == Lx
* 3: plane y == originY
* 4: plane y == Ly
"""
for n in (nx, ny):
if n <= 0 or n % 1:
raise ValueError("Number of cells must be a postive integer")
xcoords = np.linspace(originX, Lx, nx + 1, dtype=np.double)
ycoords = np.linspace(originY, Ly, ny + 1, dtype=np.double)
return TensorRectangleMesh(
xcoords,
ycoords,
quadrilateral=quadrilateral,
reorder=reorder,
diagonal=diagonal,
distribution_parameters=distribution_parameters,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
def TensorRectangleMesh(
xcoords,
ycoords,
quadrilateral=False,
reorder=None,
diagonal="left",
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a rectangular mesh
:arg xcoords: mesh points for the x direction
:arg ycoords: mesh points for the y direction
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg diagonal: For triangular meshes, should the diagonal got
from bottom left to top right (``"right"``), or top left to
bottom right (``"left"``), or put in both diagonals (``"crossed"``).
The boundary edges in this mesh are numbered as follows:
* 1: plane x == xcoords[0]
* 2: plane x == xcoords[-1]
* 3: plane y == ycoords[0]
* 4: plane y == ycoords[-1]
"""
xcoords = np.unique(xcoords)
ycoords = np.unique(ycoords)
nx = np.size(xcoords) - 1
ny = np.size(ycoords) - 1
for n in (nx, ny):
if n <= 0:
raise ValueError("Number of cells must be a postive integer")
coords = np.asarray(np.meshgrid(xcoords, ycoords)).swapaxes(0, 2).reshape(-1, 2)
# cell vertices
i, j = np.meshgrid(np.arange(nx, dtype=np.int32), np.arange(ny, dtype=np.int32))
if not quadrilateral and diagonal == "crossed":
xs = 0.5 * (xcoords[1:] + xcoords[:-1])
ys = 0.5 * (ycoords[1:] + ycoords[:-1])
extra = np.asarray(np.meshgrid(xs, ys)).swapaxes(0, 2).reshape(-1, 2)
coords = np.vstack([coords, extra])
#
# 2-----3
# | \ / |
# | 4 |
# | / \ |
# 0-----1
cells = [
i * (ny + 1) + j,
i * (ny + 1) + j + 1,
(i + 1) * (ny + 1) + j,
(i + 1) * (ny + 1) + j + 1,
(nx + 1) * (ny + 1) + i * ny + j,
]
cells = np.asarray(cells).swapaxes(0, 2).reshape(-1, 5)
idx = [0, 1, 4, 0, 2, 4, 2, 3, 4, 3, 1, 4]
cells = cells[:, idx].reshape(-1, 3)
else:
cells = [
i * (ny + 1) + j,
i * (ny + 1) + j + 1,
(i + 1) * (ny + 1) + j + 1,
(i + 1) * (ny + 1) + j,
]
cells = np.asarray(cells).swapaxes(0, 2).reshape(-1, 4)
if not quadrilateral:
if diagonal == "left":
idx = [0, 1, 3, 1, 2, 3]
elif diagonal == "right":
idx = [0, 1, 2, 0, 2, 3]
else:
raise ValueError("Unrecognised value for diagonal '%r'", diagonal)
# two cells per cell above...
cells = cells[:, idx].reshape(-1, 3)
plex = mesh.plex_from_cell_list(
2, cells, coords, comm, mesh._generate_default_mesh_topology_name(name)
)
# mark boundary facets
plex.createLabel(dmcommon.FACE_SETS_LABEL)
plex.markBoundaryFaces("boundary_faces")
coords = plex.getCoordinates()
coord_sec = plex.getCoordinateSection()
if plex.getStratumSize("boundary_faces", 1) > 0:
boundary_faces = plex.getStratumIS("boundary_faces", 1).getIndices()
xtol = 0.5 * min(xcoords[1] - xcoords[0], xcoords[-1] - xcoords[-2])
ytol = 0.5 * min(ycoords[1] - ycoords[0], ycoords[-1] - ycoords[-2])
x0 = xcoords[0]
x1 = xcoords[-1]
y0 = ycoords[0]
y1 = ycoords[-1]
for face in boundary_faces:
face_coords = plex.vecGetClosure(coord_sec, coords, face)
if abs(face_coords[0] - x0) < xtol and abs(face_coords[2] - x0) < xtol:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 1)
if abs(face_coords[0] - x1) < xtol and abs(face_coords[2] - x1) < xtol:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 2)
if abs(face_coords[1] - y0) < ytol and abs(face_coords[3] - y0) < ytol:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 3)
if abs(face_coords[1] - y1) < ytol and abs(face_coords[3] - y1) < ytol:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 4)
plex.removeLabel("boundary_faces")
m = mesh.Mesh(
plex,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
[docs]
@PETSc.Log.EventDecorator()
def SquareMesh(
nx,
ny,
L,
reorder=None,
quadrilateral=False,
diagonal="left",
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a square mesh
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg L: The extent in the x and y directions
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The boundary edges in this mesh are numbered as follows:
* 1: plane x == 0
* 2: plane x == L
* 3: plane y == 0
* 4: plane y == L
"""
return RectangleMesh(
nx,
ny,
L,
L,
reorder=reorder,
quadrilateral=quadrilateral,
diagonal=diagonal,
distribution_parameters=distribution_parameters,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def UnitSquareMesh(
nx,
ny,
reorder=None,
diagonal="left",
quadrilateral=False,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a unit square mesh
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The boundary edges in this mesh are numbered as follows:
* 1: plane x == 0
* 2: plane x == 1
* 3: plane y == 0
* 4: plane y == 1
"""
return SquareMesh(
nx,
ny,
1,
reorder=reorder,
quadrilateral=quadrilateral,
diagonal=diagonal,
distribution_parameters=distribution_parameters,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def PeriodicRectangleMesh(
nx,
ny,
Lx,
Ly,
direction="both",
quadrilateral=False,
reorder=None,
distribution_parameters=None,
diagonal=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a periodic rectangular mesh
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg Lx: The extent in the x direction
:arg Ly: The extent in the y direction
:arg direction: The direction of the periodicity, one of
``"both"``, ``"x"`` or ``"y"``.
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg diagonal: (optional), one of ``"crossed"``, ``"left"``, ``"right"``.
Not valid for quad meshes. Only used for direction ``"x"`` or direction ``"y"``.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
If direction == "x" the boundary edges in this mesh are numbered as follows:
* 1: plane y == 0
* 2: plane y == Ly
If direction == "y" the boundary edges are:
* 1: plane x == 0
* 2: plane x == Lx
"""
if direction == "both" and ny == 1 and quadrilateral:
return OneElementThickMesh(
nx,
Lx,
Ly,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
if direction not in ("both", "x", "y"):
raise ValueError(
"Cannot have a periodic mesh with periodicity '%s'" % direction
)
if direction != "both":
return PartiallyPeriodicRectangleMesh(
nx,
ny,
Lx,
Ly,
direction=direction,
quadrilateral=quadrilateral,
reorder=reorder,
distribution_parameters=distribution_parameters,
diagonal=diagonal,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
if nx < 3 or ny < 3:
raise ValueError(
"2D periodic meshes with fewer than 3 cells in each direction are not currently supported"
)
m = TorusMesh(
nx,
ny,
1.0,
0.5,
quadrilateral=quadrilateral,
reorder=reorder_noop,
distribution_parameters=distribution_parameters_no_overlap,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
coord_family = "DQ" if quadrilateral else "DG"
cell = "quadrilateral" if quadrilateral else "triangle"
coord_fs = VectorFunctionSpace(
m, FiniteElement(coord_family, cell, 1, variant="equispaced"), dim=2
)
new_coordinates = Function(
coord_fs, name=mesh._generate_default_mesh_coordinates_name(name)
)
x, y, z = SpatialCoordinate(m)
eps = 1.e-14
indicator_y = Function(FunctionSpace(m, coord_family, 0))
indicator_y.interpolate(conditional(gt(real(y), 0), 0., 1.))
x_coord = Function(FunctionSpace(m, coord_family, 1, variant="equispaced"))
x_coord.interpolate(
# Periodic break.
conditional(And(gt(real(eps), real(abs(y))), gt(real(x), 0.)), indicator_y,
# Unwrap rest of circle.
atan2(real(-y), real(-x))/(2*pi)+0.5)
)
phi_coord = as_vector([cos(2*pi*x_coord), sin(2*pi*x_coord)])
dr = dot(as_vector((x, y))-phi_coord, phi_coord)
indicator_z = Function(FunctionSpace(m, coord_family, 0))
indicator_z.interpolate(conditional(gt(real(z), 0), 0., 1.))
new_coordinates.interpolate(as_vector((
x_coord * Lx,
# Periodic break.
conditional(And(gt(real(eps), real(abs(z))), gt(real(dr), 0.)), indicator_z,
# Unwrap rest of circle.
atan2(real(-z), real(-dr))/(2*pi)+0.5) * Ly
)))
return _postprocess_periodic_mesh(new_coordinates,
comm,
distribution_parameters,
reorder,
name,
distribution_name,
permutation_name)
[docs]
@PETSc.Log.EventDecorator()
def PeriodicSquareMesh(
nx,
ny,
L,
direction="both",
quadrilateral=False,
reorder=None,
distribution_parameters=None,
diagonal=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a periodic square mesh
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg L: The extent in the x and y directions
:arg direction: The direction of the periodicity, one of
``"both"``, ``"x"`` or ``"y"``.
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg diagonal: (optional), one of ``"crossed"``, ``"left"``, ``"right"``.
Not valid for quad meshes.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
If direction == "x" the boundary edges in this mesh are numbered as follows:
* 1: plane y == 0
* 2: plane y == L
If direction == "y" the boundary edges are:
* 1: plane x == 0
* 2: plane x == L
"""
return PeriodicRectangleMesh(
nx,
ny,
L,
L,
direction=direction,
quadrilateral=quadrilateral,
reorder=reorder,
distribution_parameters=distribution_parameters,
diagonal=diagonal,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def PeriodicUnitSquareMesh(
nx,
ny,
direction="both",
reorder=None,
quadrilateral=False,
distribution_parameters=None,
diagonal=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a periodic unit square mesh
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg direction: The direction of the periodicity, one of
``"both"``, ``"x"`` or ``"y"``.
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg diagonal: (optional), one of ``"crossed"``, ``"left"``, ``"right"``.
Not valid for quad meshes.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
If direction == "x" the boundary edges in this mesh are numbered as follows:
* 1: plane y == 0
* 2: plane y == 1
If direction == "y" the boundary edges are:
* 1: plane x == 0
* 2: plane x == 1
"""
return PeriodicSquareMesh(
nx,
ny,
1.0,
direction=direction,
reorder=reorder,
quadrilateral=quadrilateral,
distribution_parameters=distribution_parameters,
diagonal=diagonal,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def CircleManifoldMesh(
ncells,
radius=1,
degree=1,
distribution_parameters=None,
reorder=False,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generated a 1D mesh of the circle, immersed in 2D.
:arg ncells: number of cells the circle should be
divided into (min 3)
:kwarg radius: (optional) radius of the circle to approximate.
:kwarg degree: polynomial degree of coordinate space (e.g.,
cells are straight line segments if degree=1).
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
if ncells < 3:
raise ValueError("CircleManifoldMesh must have at least three cells")
vertices = radius * np.column_stack(
(
np.cos(np.arange(ncells, dtype=np.double) * (2 * np.pi / ncells)),
np.sin(np.arange(ncells, dtype=np.double) * (2 * np.pi / ncells)),
)
)
cells = np.column_stack(
(
np.arange(0, ncells, dtype=np.int32),
np.roll(np.arange(0, ncells, dtype=np.int32), -1),
)
)
plex = mesh.plex_from_cell_list(
1, cells, vertices, comm, mesh._generate_default_mesh_topology_name(name)
)
m = mesh.Mesh(
plex,
dim=2,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
if degree > 1:
new_coords = function.Function(
functionspace.VectorFunctionSpace(m, "CG", degree)
)
new_coords.interpolate(ufl.SpatialCoordinate(m))
# "push out" to circle
new_coords.dat.data[:] *= (
radius / np.linalg.norm(new_coords.dat.data, axis=1)
).reshape(-1, 1)
m = mesh.Mesh(
new_coords,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
m._radius = radius
return m
[docs]
@PETSc.Log.EventDecorator()
def UnitDiskMesh(
refinement_level=0,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of the unit disk in 2D
:kwarg refinement_level: optional number of refinements (0 is a diamond)
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
vertices = np.array(
[[0, 0], [1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]],
dtype=np.double,
)
cells = np.array(
[
[0, 1, 2],
[0, 2, 3],
[0, 3, 4],
[0, 4, 5],
[0, 5, 6],
[0, 6, 7],
[0, 7, 8],
[0, 8, 1],
],
np.int32,
)
plex = mesh.plex_from_cell_list(
2, cells, vertices, comm, mesh._generate_default_mesh_topology_name(name)
)
# mark boundary facets
plex.createLabel(dmcommon.FACE_SETS_LABEL)
plex.markBoundaryFaces("boundary_faces")
if plex.getStratumSize("boundary_faces", 1) > 0:
boundary_faces = plex.getStratumIS("boundary_faces", 1).getIndices()
for face in boundary_faces:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 1)
plex.removeLabel("boundary_faces")
plex.setRefinementUniform(True)
for i in range(refinement_level):
plex = plex.refine()
coords = plex.getCoordinatesLocal().array.reshape(-1, 2)
for x in coords:
norm = np.sqrt(np.dot(x, x))
if norm > 1.0 / (1 << (refinement_level + 1)):
t = np.max(np.abs(x)) / norm
x[:] *= t
m = mesh.Mesh(
plex,
dim=2,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
[docs]
@PETSc.Log.EventDecorator()
def UnitBallMesh(
refinement_level=0,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of the unit ball in 3D
:kwarg refinement_level: optional number of refinements (0 is an octahedron)
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional MPI communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
vertices = np.array(
[
[0, 0, 0],
[1, 0, 0],
[0, 1, 0],
[0, 0, 1],
[-1, 0, 0],
[0, -1, 0],
[0, 0, -1],
],
dtype=np.double,
)
cells = np.array(
[
[0, 1, 2, 3],
[0, 2, 4, 3],
[0, 4, 5, 3],
[0, 5, 1, 3],
[0, 2, 1, 6],
[0, 4, 2, 6],
[0, 5, 4, 6],
[0, 1, 5, 6],
],
np.int32,
)
plex = mesh.plex_from_cell_list(
3, cells, vertices, comm, mesh._generate_default_mesh_topology_name(name)
)
plex.createLabel(dmcommon.FACE_SETS_LABEL)
plex.markBoundaryFaces("boundary_faces")
if plex.getStratumSize("boundary_faces", 1) > 0:
boundary_faces = plex.getStratumIS("boundary_faces", 1).getIndices()
for face in boundary_faces:
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 1)
plex.removeLabel("boundary_faces")
plex.setRefinementUniform(True)
for i in range(refinement_level):
plex = plex.refine()
coords = plex.getCoordinatesLocal().array.reshape(-1, 3)
for x in coords:
norm = np.sqrt(np.dot(x, x))
if norm > 1.0 / (1 << (refinement_level + 1)):
t = np.sum(np.abs(x)) / norm
x[:] *= t
m = mesh.Mesh(
plex,
dim=3,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
[docs]
@PETSc.Log.EventDecorator()
def UnitTetrahedronMesh(
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of the reference tetrahedron.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
coords = [[0.0, 0.0, 0.0], [1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
cells = [[0, 1, 2, 3]]
plex = mesh.plex_from_cell_list(
3, cells, coords, comm, mesh._generate_default_mesh_topology_name(name)
)
m = mesh.Mesh(
plex,
reorder=False,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
[docs]
def TensorBoxMesh(
xcoords,
ycoords,
zcoords,
reorder=None,
distribution_parameters=None,
diagonal="default",
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of a 3D box.
:arg xcoords: Location of nodes in the x direction
:arg ycoords: Location of nodes in the y direction
:arg zcoords: Location of nodes in the z direction
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg diagonal: Two ways of cutting hexadra, should be cut into 6
tetrahedra (``"default"``), or 5 tetrahedra thus less biased
(``"crossed"``)
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg comm: Optional communicator to build the mesh on.
The boundary surfaces are numbered as follows:
* 1: plane x == xcoords[0]
* 2: plane x == xcoords[-1]
* 3: plane y == ycoords[0]
* 4: plane y == ycoords[-1]
* 5: plane z == zcoords[0]
* 6: plane z == zcoords[-1]
"""
xcoords = np.unique(xcoords)
ycoords = np.unique(ycoords)
zcoords = np.unique(zcoords)
nx = np.size(xcoords)-1
ny = np.size(ycoords)-1
nz = np.size(zcoords)-1
for n in (nx, ny, nz):
if n <= 0 or n % 1:
raise ValueError("Number of cells must be a postive integer")
# X moves fastest, then Y, then Z
coords = (
np.asarray(np.meshgrid(xcoords, ycoords, zcoords)).swapaxes(0, 3).reshape(-1, 3)
)
i, j, k = np.meshgrid(
np.arange(nx, dtype=np.int32),
np.arange(ny, dtype=np.int32),
np.arange(nz, dtype=np.int32),
)
if diagonal == "default":
v0 = k * (nx + 1) * (ny + 1) + j * (nx + 1) + i
v1 = v0 + 1
v2 = v0 + (nx + 1)
v3 = v1 + (nx + 1)
v4 = v0 + (nx + 1) * (ny + 1)
v5 = v1 + (nx + 1) * (ny + 1)
v6 = v2 + (nx + 1) * (ny + 1)
v7 = v3 + (nx + 1) * (ny + 1)
cells = [
[v0, v1, v3, v7],
[v0, v1, v7, v5],
[v0, v5, v7, v4],
[v0, v3, v2, v7],
[v0, v6, v4, v7],
[v0, v2, v6, v7],
]
cells = np.asarray(cells).reshape(-1, ny, nx, nz).swapaxes(0, 3).reshape(-1, 4)
elif diagonal == "crossed":
v0 = k * (nx + 1) * (ny + 1) + j * (nx + 1) + i
v1 = v0 + 1
v2 = v0 + (nx + 1)
v3 = v1 + (nx + 1)
v4 = v0 + (nx + 1) * (ny + 1)
v5 = v1 + (nx + 1) * (ny + 1)
v6 = v2 + (nx + 1) * (ny + 1)
v7 = v3 + (nx + 1) * (ny + 1)
# There are only five tetrahedra in this cutting of hexahedra
cells = [
[v0, v1, v2, v4],
[v1, v7, v5, v4],
[v1, v2, v3, v7],
[v2, v4, v6, v7],
[v1, v2, v7, v4],
]
cells = np.asarray(cells).reshape(-1, ny, nx, nz).swapaxes(0, 3).reshape(-1, 4)
raise NotImplementedError(
"The crossed cutting of hexahedra has a broken connectivity issue for Pk (k>1) elements"
)
else:
raise ValueError("Unrecognised value for diagonal '%r'", diagonal)
plex = mesh.plex_from_cell_list(
3, cells, coords, comm, mesh._generate_default_mesh_topology_name(name)
)
nvert = 3 # num. vertices on facet
# Apply boundary IDs
plex.createLabel(dmcommon.FACE_SETS_LABEL)
plex.markBoundaryFaces("boundary_faces")
coords = plex.getCoordinates()
coord_sec = plex.getCoordinateSection()
cdim = plex.getCoordinateDim()
assert cdim == 3
if plex.getStratumSize("boundary_faces", 1) > 0:
boundary_faces = plex.getStratumIS("boundary_faces", 1).getIndices()
xtol = 0.5 * min(xcoords[1]-xcoords[0], xcoords[-1] - xcoords[-2])
ytol = 0.5 * min(ycoords[1]-ycoords[0], ycoords[-1] - ycoords[-2])
ztol = 0.5 * min(zcoords[1]-zcoords[0], zcoords[-1] - zcoords[-2])
x0 = xcoords[0]
x1 = xcoords[-1]
y0 = ycoords[0]
y1 = ycoords[-1]
z0 = zcoords[0]
z1 = zcoords[-1]
for face in boundary_faces:
face_coords = plex.vecGetClosure(coord_sec, coords, face)
if all([abs(face_coords[0 + cdim * i] - x0) < xtol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 1)
if all([abs(face_coords[0 + cdim * i] - x1) < xtol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 2)
if all([abs(face_coords[1 + cdim * i] - y0) < ytol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 3)
if all([abs(face_coords[1 + cdim * i] - y1) < ytol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 4)
if all([abs(face_coords[2 + cdim * i] - z0) < ztol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 5)
if all([abs(face_coords[2 + cdim * i] - z1) < ztol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 6)
plex.removeLabel("boundary_faces")
m = mesh.Mesh(
plex,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
[docs]
@PETSc.Log.EventDecorator()
def BoxMesh(
nx,
ny,
nz,
Lx,
Ly,
Lz,
hexahedral=False,
reorder=None,
distribution_parameters=None,
diagonal="default",
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of a 3D box.
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg nz: The number of cells in the z direction
:arg Lx: The extent in the x direction
:arg Ly: The extent in the y direction
:arg Lz: The extent in the z direction
:kwarg hexahedral: (optional), creates hexahedral mesh.
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg diagonal: Two ways of cutting hexadra, should be cut into 6
tetrahedra (``"default"``), or 5 tetrahedra thus less biased
(``"crossed"``)
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg comm: Optional communicator to build the mesh on.
The boundary surfaces are numbered as follows:
* 1: plane x == 0
* 2: plane x == Lx
* 3: plane y == 0
* 4: plane y == Ly
* 5: plane z == 0
* 6: plane z == Lz
"""
for n in (nx, ny, nz):
if n <= 0 or n % 1:
raise ValueError("Number of cells must be a postive integer")
if hexahedral:
plex = PETSc.DMPlex().createBoxMesh((nx, ny, nz), lower=(0., 0., 0.), upper=(Lx, Ly, Lz), simplex=False, periodic=False, interpolate=True, comm=comm)
plex.removeLabel(dmcommon.FACE_SETS_LABEL)
nvert = 4 # num. vertices on faect
# Apply boundary IDs
plex.createLabel(dmcommon.FACE_SETS_LABEL)
plex.markBoundaryFaces("boundary_faces")
coords = plex.getCoordinates()
coord_sec = plex.getCoordinateSection()
cdim = plex.getCoordinateDim()
assert cdim == 3
if plex.getStratumSize("boundary_faces", 1) > 0:
boundary_faces = plex.getStratumIS("boundary_faces", 1).getIndices()
xtol = Lx / (2 * nx)
ytol = Ly / (2 * ny)
ztol = Lz / (2 * nz)
for face in boundary_faces:
face_coords = plex.vecGetClosure(coord_sec, coords, face)
if all([abs(face_coords[0 + cdim * i]) < xtol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 1)
if all([abs(face_coords[0 + cdim * i] - Lx) < xtol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 2)
if all([abs(face_coords[1 + cdim * i]) < ytol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 3)
if all([abs(face_coords[1 + cdim * i] - Ly) < ytol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 4)
if all([abs(face_coords[2 + cdim * i]) < ztol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 5)
if all([abs(face_coords[2 + cdim * i] - Lz) < ztol for i in range(nvert)]):
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 6)
plex.removeLabel("boundary_faces")
m = mesh.Mesh(
plex,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
else:
xcoords = np.linspace(0, Lx, nx + 1, dtype=np.double)
ycoords = np.linspace(0, Ly, ny + 1, dtype=np.double)
zcoords = np.linspace(0, Lz, nz + 1, dtype=np.double)
return TensorBoxMesh(
xcoords,
ycoords,
zcoords,
reorder=reorder,
distribution_parameters=distribution_parameters,
diagonal=diagonal,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def CubeMesh(
nx,
ny,
nz,
L,
hexahedral=False,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of a cube
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg nz: The number of cells in the z direction
:arg L: The extent in the x, y and z directions
:kwarg hexahedral: (optional), creates hexahedral mesh.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The boundary surfaces are numbered as follows:
* 1: plane x == 0
* 2: plane x == L
* 3: plane y == 0
* 4: plane y == L
* 5: plane z == 0
* 6: plane z == L
"""
return BoxMesh(
nx,
ny,
nz,
L,
L,
L,
hexahedral=hexahedral,
reorder=reorder,
distribution_parameters=distribution_parameters,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def UnitCubeMesh(
nx,
ny,
nz,
hexahedral=False,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a mesh of a unit cube
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg nz: The number of cells in the z direction
:kwarg hexahedral: (optional), creates hexahedral mesh.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The boundary surfaces are numbered as follows:
* 1: plane x == 0
* 2: plane x == 1
* 3: plane y == 0
* 4: plane y == 1
* 5: plane z == 0
* 6: plane z == 1
"""
return CubeMesh(
nx,
ny,
nz,
1,
hexahedral=hexahedral,
reorder=reorder,
distribution_parameters=distribution_parameters,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def PeriodicBoxMesh(
nx,
ny,
nz,
Lx,
Ly,
Lz,
directions=(True, True, True),
hexahedral=False,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a periodic mesh of a 3D box.
Parameters
----------
nx : int
Number of cells in the x direction.
ny : int
Number of cells in the y direction.
nz : int
Number of cells in the z direction.
Lx : float
Extent in the x direction.
Ly : float
Extent in the y direction.
Lz : float
Extent in the z direction.
directions : list or tuple
Directions of periodicity.
hexahedral : bool
Whether to make hexahedral mesh or not.
reorder : bool or None
Whether to reorder the mesh.
distribution_parameters : dict or None
Options controlling mesh distribution, see :func:`.Mesh` for details.
comm :
Communicator to build the mesh on.
name : str
Name of the mesh.
distribution_name : str or None
Name of parallel distribution used when checkpointing;
if `None`, the name is automatically generated.
permutation_name : str or None
Name of entity permutation (reordering) used when checkpointing;
if `None`, the name is automatically generated.
Returns
-------
MeshGeometry
The mesh.
Notes
-----
The boundary surfaces are numbered as follows:
* 1: plane x == 0
* 2: plane x == 1
* 3: plane y == 0
* 4: plane y == 1
* 5: plane z == 0
* 6: plane z == 1
where periodic surfaces are regarded as interior, for which dS integral is to be used.
"""
for n in (nx, ny, nz):
if n < 3:
raise ValueError(
"3D periodic meshes with fewer than 3 cells are not currently supported"
)
if hexahedral:
if len(directions) != 3:
raise ValueError(f"directions must have exactly dim (=3) elements : Got {directions}")
plex = PETSc.DMPlex().createBoxMesh(
(nx, ny, nz),
lower=(0., 0., 0.),
upper=(Lx, Ly, Lz),
simplex=False,
periodic=directions,
interpolate=True,
sparseLocalize=False,
comm=comm,
)
m = mesh.Mesh(
plex,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm)
x, y, z = SpatialCoordinate(m)
V = FunctionSpace(m, "Q", 2)
eps = min([Lx / nx, Ly / ny, Lz / nz]) / 1000.
if directions[0]: # x
fx0 = Function(V).interpolate(conditional(Or(x < eps, x > Lx - eps), 1., 0.))
fx1 = fx0
else:
fx0 = Function(V).interpolate(conditional(x < eps, 1., 0.))
fx1 = Function(V).interpolate(conditional(x > Lx - eps, 1., 0.))
if directions[1]: # y
fy0 = Function(V).interpolate(conditional(Or(y < eps, y > Ly - eps), 1., 0.))
fy1 = fy0
else:
fy0 = Function(V).interpolate(conditional(y < eps, 1., 0.))
fy1 = Function(V).interpolate(conditional(y > Ly - eps, 1., 0.))
if directions[2]: # z
fz0 = Function(V).interpolate(conditional(Or(z < eps, z > Lz - eps), 1., 0.))
fz1 = fz0
else:
fz0 = Function(V).interpolate(conditional(z < eps, 1., 0.))
fz1 = Function(V).interpolate(conditional(z > Lz - eps, 1., 0.))
return mesh.RelabeledMesh(m, [fx0, fx1, fy0, fy1, fz0, fz1], [1, 2, 3, 4, 5, 6], name=name)
else:
if tuple(directions) != (True, True, True):
raise NotImplementedError("Can only specify directions with hexahedral = True")
xcoords = np.arange(0.0, Lx, Lx / nx, dtype=np.double)
ycoords = np.arange(0.0, Ly, Ly / ny, dtype=np.double)
zcoords = np.arange(0.0, Lz, Lz / nz, dtype=np.double)
coords = (
np.asarray(np.meshgrid(xcoords, ycoords, zcoords)).swapaxes(0, 3).reshape(-1, 3)
)
i, j, k = np.meshgrid(
np.arange(nx, dtype=np.int32),
np.arange(ny, dtype=np.int32),
np.arange(nz, dtype=np.int32),
)
v0 = k * nx * ny + j * nx + i
v1 = k * nx * ny + j * nx + (i + 1) % nx
v2 = k * nx * ny + ((j + 1) % ny) * nx + i
v3 = k * nx * ny + ((j + 1) % ny) * nx + (i + 1) % nx
v4 = ((k + 1) % nz) * nx * ny + j * nx + i
v5 = ((k + 1) % nz) * nx * ny + j * nx + (i + 1) % nx
v6 = ((k + 1) % nz) * nx * ny + ((j + 1) % ny) * nx + i
v7 = ((k + 1) % nz) * nx * ny + ((j + 1) % ny) * nx + (i + 1) % nx
cells = [
[v0, v1, v3, v7],
[v0, v1, v7, v5],
[v0, v5, v7, v4],
[v0, v3, v2, v7],
[v0, v6, v4, v7],
[v0, v2, v6, v7],
]
cells = np.asarray(cells).reshape(-1, ny, nx, nz).swapaxes(0, 3).reshape(-1, 4)
plex = mesh.plex_from_cell_list(
3, cells, coords, comm, mesh._generate_default_mesh_topology_name(name)
)
m = mesh.Mesh(
plex,
reorder=reorder_noop,
distribution_parameters=distribution_parameters_no_overlap,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
new_coordinates = Function(
VectorFunctionSpace(
m, FiniteElement("DG", tetrahedron, 1, variant="equispaced")
),
name=mesh._generate_default_mesh_coordinates_name(name),
)
new_coordinates.interpolate(m.coordinates)
coords_by_cell = new_coordinates.dat.data.reshape((-1, 4, 3)).transpose(1, 0, 2)
# ensure we really got a view:
assert coords_by_cell.base is new_coordinates.dat.data.base
# Find the cells that are too big in each direction because they are
# wrapped.
cell_is_wrapped = (
(coords_by_cell.max(axis=0) - coords_by_cell.min(axis=0))
/ (Lx/nx, Ly/ny, Lz/nz) > 1.1
)
# Move wrapped coordinates to the other end of the domain.
for i, extent in enumerate((Lx, Ly, Lz)):
coords = coords_by_cell[:, :, i]
coords[np.logical_and(cell_is_wrapped[:, i], np.isclose(coords, 0))] \
= extent
return _postprocess_periodic_mesh(new_coordinates,
comm,
distribution_parameters,
reorder,
name,
distribution_name,
permutation_name)
[docs]
@PETSc.Log.EventDecorator()
def PeriodicUnitCubeMesh(
nx,
ny,
nz,
directions=(True, True, True),
hexahedral=False,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a periodic mesh of a unit cube
Parameters
----------
nx : int
Number of cells in the x direction.
ny : int
Number of cells in the y direction.
nz : int
Number of cells in the z direction.
directions : list or tuple
Directions of periodicity.
hexahedral : bool
Whether to make hexahedral mesh or not.
reorder : bool or None
Should the mesh be reordered?
distribution_parameters : dict or None
Options controlling mesh distribution, see :func:`.Mesh` for details.
comm :
Communicator to build the mesh on.
name : str
Name of the mesh.
distribution_name : str or None
Name of parallel distribution used when checkpointing;
if `None`, the name is automatically generated.
permutation_name : str or None
Name of entity permutation (reordering) used when checkpointing;
if `None`, the name is automatically generated.
Returns
-------
MeshGeometry
The mesh.
Notes
-----
The boundary surfaces are numbered as follows:
* 1: plane x == 0
* 2: plane x == 1
* 3: plane y == 0
* 4: plane y == 1
* 5: plane z == 0
* 6: plane z == 1
where periodic surfaces are regarded as interior, for which dS integral is to be used.
"""
return PeriodicBoxMesh(
nx,
ny,
nz,
1.0,
1.0,
1.0,
directions=directions,
hexahedral=hexahedral,
reorder=reorder,
distribution_parameters=distribution_parameters,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def IcosahedralSphereMesh(
radius,
refinement_level=0,
degree=1,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate an icosahedral approximation to the surface of the
sphere.
:arg radius: The radius of the sphere to approximate.
For a radius R the edge length of the underlying
icosahedron will be.
.. math::
a = \\frac{R}{\\sin(2 \\pi / 5)}
:kwarg refinement_level: optional number of refinements (0 is an
icosahedron).
:kwarg degree: polynomial degree of coordinate space (e.g.,
flat triangles if degree=1).
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
if refinement_level < 0 or refinement_level % 1:
raise RuntimeError("Number of refinements must be a non-negative integer")
if degree < 1:
raise ValueError("Mesh coordinate degree must be at least 1")
from math import sqrt
phi = (1 + sqrt(5)) / 2
# vertices of an icosahedron with an edge length of 2
vertices = np.array(
[
[-1, phi, 0],
[1, phi, 0],
[-1, -phi, 0],
[1, -phi, 0],
[0, -1, phi],
[0, 1, phi],
[0, -1, -phi],
[0, 1, -phi],
[phi, 0, -1],
[phi, 0, 1],
[-phi, 0, -1],
[-phi, 0, 1],
],
dtype=np.double,
)
# faces of the base icosahedron
faces = np.array(
[
[0, 11, 5],
[0, 5, 1],
[0, 1, 7],
[0, 7, 10],
[0, 10, 11],
[1, 5, 9],
[5, 11, 4],
[11, 10, 2],
[10, 7, 6],
[7, 1, 8],
[3, 9, 4],
[3, 4, 2],
[3, 2, 6],
[3, 6, 8],
[3, 8, 9],
[4, 9, 5],
[2, 4, 11],
[6, 2, 10],
[8, 6, 7],
[9, 8, 1],
],
dtype=np.int32,
)
plex = mesh.plex_from_cell_list(2, faces, vertices, comm)
plex.setRefinementUniform(True)
for i in range(refinement_level):
plex = plex.refine()
plex.setName(mesh._generate_default_mesh_topology_name(name))
coords = plex.getCoordinatesLocal().array.reshape(-1, 3)
scale = (radius / np.linalg.norm(coords, axis=1)).reshape(-1, 1)
coords *= scale
m = mesh.Mesh(
plex,
dim=3,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
if degree > 1:
new_coords = function.Function(
functionspace.VectorFunctionSpace(m, "CG", degree)
)
new_coords.interpolate(ufl.SpatialCoordinate(m))
# "push out" to sphere
new_coords.dat.data[:] *= (
radius / np.linalg.norm(new_coords.dat.data, axis=1)
).reshape(-1, 1)
m = mesh.Mesh(
new_coords,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
m._radius = radius
return m
[docs]
@PETSc.Log.EventDecorator()
def UnitIcosahedralSphereMesh(
refinement_level=0,
degree=1,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate an icosahedral approximation to the unit sphere.
:kwarg refinement_level: optional number of refinements (0 is an
icosahedron).
:kwarg degree: polynomial degree of coordinate space (e.g.,
flat triangles if degree=1).
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
return IcosahedralSphereMesh(
1.0,
refinement_level=refinement_level,
degree=degree,
reorder=reorder,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
# mesh is mainly used as a utility, so it's unnecessary to annotate the construction
# in this case.
[docs]
@PETSc.Log.EventDecorator()
@no_annotations
def OctahedralSphereMesh(
radius,
refinement_level=0,
degree=1,
hemisphere="both",
z0=0.8,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate an octahedral approximation to the surface of the
sphere.
:arg radius: The radius of the sphere to approximate.
:kwarg refinement_level: optional number of refinements (0 is an
octahedron).
:kwarg degree: polynomial degree of coordinate space (e.g.,
flat triangles if degree=1).
:kwarg hemisphere: One of "both", "north", or "south"
:kwarg z0: for abs(z/R)>z0, blend from a mesh where the higher-order
non-vertex nodes are on lines of latitude to a mesh where these nodes
are just pushed out radially from the equivalent P1 mesh.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
if refinement_level < 0 or refinement_level % 1:
raise ValueError("Number of refinements must be a non-negative integer")
if degree < 1:
raise ValueError("Mesh coordinate degree must be at least 1")
if hemisphere not in {"both", "north", "south"}:
raise ValueError("Unhandled hemisphere '%s'" % hemisphere)
# vertices of an octahedron of radius 1
vertices = np.array(
[
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0],
[-1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, -1.0],
]
)
faces = np.array(
[
[0, 1, 2],
[0, 1, 5],
[0, 2, 4],
[0, 4, 5],
[1, 2, 3],
[1, 3, 5],
[2, 3, 4],
[3, 4, 5],
],
dtype=IntType,
)
if hemisphere == "north":
vertices = vertices[[0, 1, 2, 3, 4], ...]
faces = faces[0::2, ...]
elif hemisphere == "south":
indices = [0, 1, 3, 4, 5]
vertices = vertices[indices, ...]
faces = faces[1::2, ...]
for new, idx in enumerate(indices):
faces[faces == idx] = new
plex = mesh.plex_from_cell_list(2, faces, vertices, comm)
plex.setRefinementUniform(True)
for i in range(refinement_level):
plex = plex.refine()
plex.setName(mesh._generate_default_mesh_topology_name(name))
# build the initial mesh
m = mesh.Mesh(
plex,
dim=3,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
if degree > 1:
# use it to build a higher-order mesh
m = assemble(Interpolate(ufl.SpatialCoordinate(m), VectorFunctionSpace(m, "CG", degree)))
m = mesh.Mesh(
m,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
# remap to a cone
x, y, z = ufl.SpatialCoordinate(m)
# This will DTWT on meshes with more than 26 refinement levels.
# (log_2 1e8 ~= 26.5)
tol = ufl.real(Constant(1.0e-8))
rnew = ufl.max_value(1 - abs(z), 0)
# Avoid division by zero (when rnew is zero, x & y are also zero)
x0 = ufl.conditional(ufl.lt(ufl.real(rnew), tol), 0, x / rnew)
y0 = ufl.conditional(ufl.lt(rnew, tol), 0, y / rnew)
theta = ufl.conditional(
ufl.ge(ufl.real(y0), 0), ufl.pi / 2 * (1 - x0), ufl.pi / 2.0 * (x0 - 1)
)
m.coordinates.interpolate(
ufl.as_vector([ufl.cos(theta) * rnew, ufl.sin(theta) * rnew, z])
)
# push out to a sphere
phi = ufl.pi * z / 2
# Avoid division by zero (when rnew is zero, phi is pi/2, so cos(phi) is zero).
scale = ufl.conditional(
ufl.lt(ufl.real(rnew), ufl.real(tol)), 0, ufl.cos(phi) / rnew
)
znew = ufl.sin(phi)
# Make a copy of the coordinates so that we can blend two different
# mappings near the pole
Vc = m.coordinates.function_space()
Xlatitudinal = assemble(Interpolate(
Constant(radius) * ufl.as_vector([x * scale, y * scale, znew]), Vc
))
Vlow = VectorFunctionSpace(m, "CG", 1)
Xlow = assemble(Interpolate(Xlatitudinal, Vlow))
r = ufl.sqrt(Xlow[0] ** 2 + Xlow[1] ** 2 + Xlow[2] ** 2)
Xradial = Constant(radius) * Xlow / r
s = ufl.real(abs(z) - z0) / (1 - z0)
exp = ufl.exp
taper = ufl.conditional(
ufl.gt(real(s), real(1.0 - tol)),
1.0,
ufl.conditional(
ufl.gt(real(s), real(tol)), exp(-1.0 / s) / (exp(-1.0 / s) + exp(-1.0 / (1.0 - s))), 0.0
),
)
m.coordinates.interpolate(taper * Xradial + (1 - taper) * Xlatitudinal)
m._radius = radius
return m
[docs]
@PETSc.Log.EventDecorator()
def UnitOctahedralSphereMesh(
refinement_level=0,
degree=1,
hemisphere="both",
z0=0.8,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate an octahedral approximation to the unit sphere.
:kwarg refinement_level: optional number of refinements (0 is an
octahedron).
:kwarg degree: polynomial degree of coordinate space (e.g.,
flat triangles if degree=1).
:kwarg hemisphere: One of "both", "north", or "south"
:kwarg z0: for abs(z)>z0, blend from a mesh where the higher-order
non-vertex nodes are on lines of latitude to a mesh where these nodes
are just pushed out radially from the equivalent P1 mesh.
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
return OctahedralSphereMesh(
1.0,
refinement_level=refinement_level,
degree=degree,
hemisphere=hemisphere,
z0=z0,
reorder=reorder,
distribution_parameters=distribution_parameters,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
def _cubedsphere_cells_and_coords(radius, refinement_level):
"""Generate vertex and face lists for cubed sphere"""
# We build the mesh out of 6 panels of the cube
# this allows to build the gnonomic cube transformation
# which is defined separately for each panel
# Start by making a grid of local coordinates which we use
# to map to each panel of the cubed sphere under the gnonomic
# transformation
dtheta = 2 ** (-refinement_level + 1) * np.arctan(1.0)
a = 3.0 ** (-0.5) * radius
theta = np.arange(np.arctan(-1.0), np.arctan(1.0) + dtheta, dtheta, dtype=np.double)
x = a * np.tan(theta)
Nx = x.size
# Compute panel numberings for each panel
# We use the following "flatpack" arrangement of panels
# 3
# 102
# 4
# 5
# 0 is the bottom of the cube, 5 is the top.
# All panels are numbered from left to right, top to bottom
# according to this diagram.
panel_numbering = np.zeros((6, Nx, Nx), dtype=np.int32)
# Numbering for panel 0
panel_numbering[0, :, :] = np.arange(Nx**2, dtype=np.int32).reshape(Nx, Nx)
count = panel_numbering.max() + 1
# Numbering for panel 5
panel_numbering[5, :, :] = count + np.arange(Nx**2, dtype=np.int32).reshape(
Nx, Nx
)
count = panel_numbering.max() + 1
# Numbering for panel 4 - shares top edge with 0 and bottom edge
# with 5
# interior numbering
panel_numbering[4, 1:-1, :] = count + np.arange(
Nx * (Nx - 2), dtype=np.int32
).reshape(Nx - 2, Nx)
# bottom edge
panel_numbering[4, 0, :] = panel_numbering[5, -1, :]
# top edge
panel_numbering[4, -1, :] = panel_numbering[0, 0, :]
count = panel_numbering.max() + 1
# Numbering for panel 3 - shares top edge with 5 and bottom edge
# with 0
# interior numbering
panel_numbering[3, 1:-1, :] = count + np.arange(
Nx * (Nx - 2), dtype=np.int32
).reshape(Nx - 2, Nx)
# bottom edge
panel_numbering[3, 0, :] = panel_numbering[0, -1, :]
# top edge
panel_numbering[3, -1, :] = panel_numbering[5, 0, :]
count = panel_numbering.max() + 1
# Numbering for panel 1
# interior numbering
panel_numbering[1, 1:-1, 1:-1] = count + np.arange(
(Nx - 2) ** 2, dtype=np.int32
).reshape(Nx - 2, Nx - 2)
# left edge of 1 is left edge of 5 (inverted)
panel_numbering[1, :, 0] = panel_numbering[5, ::-1, 0]
# right edge of 1 is left edge of 0
panel_numbering[1, :, -1] = panel_numbering[0, :, 0]
# top edge (excluding vertices) of 1 is left edge of 3 (downwards)
panel_numbering[1, -1, 1:-1] = panel_numbering[3, -2:0:-1, 0]
# bottom edge (excluding vertices) of 1 is left edge of 4
panel_numbering[1, 0, 1:-1] = panel_numbering[4, 1:-1, 0]
count = panel_numbering.max() + 1
# Numbering for panel 2
# interior numbering
panel_numbering[2, 1:-1, 1:-1] = count + np.arange(
(Nx - 2) ** 2, dtype=np.int32
).reshape(Nx - 2, Nx - 2)
# left edge of 2 is right edge of 0
panel_numbering[2, :, 0] = panel_numbering[0, :, -1]
# right edge of 2 is right edge of 5 (inverted)
panel_numbering[2, :, -1] = panel_numbering[5, ::-1, -1]
# bottom edge (excluding vertices) of 2 is right edge of 4 (downwards)
panel_numbering[2, 0, 1:-1] = panel_numbering[4, -2:0:-1, -1]
# top edge (excluding vertices) of 2 is right edge of 3
panel_numbering[2, -1, 1:-1] = panel_numbering[3, 1:-1, -1]
count = panel_numbering.max() + 1
# That's the numbering done.
# Set up an array for all of the mesh coordinates
Npoints = panel_numbering.max() + 1
coords = np.zeros((Npoints, 3), dtype=np.double)
lX, lY = np.meshgrid(x, x)
lX.shape = (Nx**2,)
lY.shape = (Nx**2,)
r = (a**2 + lX**2 + lY**2) ** 0.5
# Now we need to compute the gnonomic transformation
# for each of the panels
panel_numbering.shape = (6, Nx**2)
def coordinates_on_panel(panel_num, X, Y, Z):
I = panel_numbering[panel_num, :]
coords[I, 0] = radius / r * X
coords[I, 1] = radius / r * Y
coords[I, 2] = radius / r * Z
coordinates_on_panel(0, lX, lY, -a)
coordinates_on_panel(1, -a, lY, -lX)
coordinates_on_panel(2, a, lY, lX)
coordinates_on_panel(3, lX, a, lY)
coordinates_on_panel(4, lX, -a, -lY)
coordinates_on_panel(5, lX, -lY, a)
# Now we need to build the face numbering
# in local coordinates
vertex_numbers = np.arange(Nx**2, dtype=np.int32).reshape(Nx, Nx)
local_faces = np.zeros(((Nx - 1) ** 2, 4), dtype=np.int32)
local_faces[:, 0] = vertex_numbers[:-1, :-1].reshape(-1)
local_faces[:, 1] = vertex_numbers[1:, :-1].reshape(-1)
local_faces[:, 2] = vertex_numbers[1:, 1:].reshape(-1)
local_faces[:, 3] = vertex_numbers[:-1, 1:].reshape(-1)
cells = panel_numbering[:, local_faces].reshape(-1, 4)
return cells, coords
[docs]
@PETSc.Log.EventDecorator()
def CubedSphereMesh(
radius,
refinement_level=0,
degree=1,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate an cubed approximation to the surface of the
sphere.
:arg radius: The radius of the sphere to approximate.
:kwarg refinement_level: optional number of refinements (0 is a cube).
:kwarg degree: polynomial degree of coordinate space (e.g.,
bilinear quads if degree=1).
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
if refinement_level < 0 or refinement_level % 1:
raise RuntimeError("Number of refinements must be a non-negative integer")
if degree < 1:
raise ValueError("Mesh coordinate degree must be at least 1")
cells, coords = _cubedsphere_cells_and_coords(radius, refinement_level)
plex = mesh.plex_from_cell_list(
2, cells, coords, comm, mesh._generate_default_mesh_topology_name(name)
)
m = mesh.Mesh(
plex,
dim=3,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
if degree > 1:
new_coords = function.Function(
functionspace.VectorFunctionSpace(m, "Q", degree)
)
new_coords.interpolate(ufl.SpatialCoordinate(m))
# "push out" to sphere
new_coords.dat.data[:] *= (
radius / np.linalg.norm(new_coords.dat.data, axis=1)
).reshape(-1, 1)
m = mesh.Mesh(
new_coords,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
m._radius = radius
return m
[docs]
@PETSc.Log.EventDecorator()
def UnitCubedSphereMesh(
refinement_level=0,
degree=1,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a cubed approximation to the unit sphere.
:kwarg refinement_level: optional number of refinements (0 is a cube).
:kwarg degree: polynomial degree of coordinate space (e.g.,
bilinear quads if degree=1).
:kwarg reorder: (optional), should the mesh be reordered?
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
return CubedSphereMesh(
1.0,
refinement_level=refinement_level,
degree=degree,
reorder=reorder,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
[docs]
@PETSc.Log.EventDecorator()
def TorusMesh(
nR,
nr,
R,
r,
quadrilateral=False,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a toroidal mesh
:arg nR: The number of cells in the major direction (min 3)
:arg nr: The number of cells in the minor direction (min 3)
:arg R: The major radius
:arg r: The minor radius
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
"""
if nR < 3 or nr < 3:
raise ValueError("Must have at least 3 cells in each direction")
for n in (nR, nr):
if n % 1:
raise RuntimeError("Number of cells must be an integer")
# gives an array [[0, 0], [0, 1], ..., [1, 0], [1, 1], ...]
idx_temp = (
np.asarray(np.meshgrid(np.arange(nR), np.arange(nr)))
.swapaxes(0, 2)
.reshape(-1, 2)
)
# vertices - standard formula for (x, y, z), see Wikipedia
vertices = np.asarray(
np.column_stack(
(
(R + r * np.cos(idx_temp[:, 1] * (2 * np.pi / nr)))
* np.cos(idx_temp[:, 0] * (2 * np.pi / nR)),
(R + r * np.cos(idx_temp[:, 1] * (2 * np.pi / nr)))
* np.sin(idx_temp[:, 0] * (2 * np.pi / nR)),
r * np.sin(idx_temp[:, 1] * (2 * np.pi / nr)),
)
),
dtype=np.double,
)
# cell vertices
i, j = np.meshgrid(np.arange(nR, dtype=np.int32), np.arange(nr, dtype=np.int32))
i = i.reshape(-1) # Miklos's suggestion to make the code
j = j.reshape(-1) # less impenetrable
cells = [
i * nr + j,
i * nr + (j + 1) % nr,
((i + 1) % nR) * nr + (j + 1) % nr,
((i + 1) % nR) * nr + j,
]
cells = np.column_stack(cells)
if not quadrilateral:
# two cells per cell above...
cells = cells[:, [0, 1, 3, 1, 2, 3]].reshape(-1, 3)
plex = mesh.plex_from_cell_list(
2, cells, vertices, comm, mesh._generate_default_mesh_topology_name(name)
)
m = mesh.Mesh(
plex,
dim=3,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
return m
[docs]
@PETSc.Log.EventDecorator()
def AnnulusMesh(
R,
r,
nr=4,
nt=32,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate an annulus mesh periodically extruding an interval mesh
:arg R: The outer radius
:arg r: The inner radius
:kwarg nr: (optional), number of cells in the radial direction
:kwarg nt: (optional), number of cells in the circumferential direction (min 3)
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if ``None``, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if ``None``, the name is automatically
generated.
"""
if nt < 3:
raise ValueError("Must have at least 3 cells in the circumferential direction")
base_name = name + "_base"
base = IntervalMesh(nr,
r,
right=R,
distribution_parameters=distribution_parameters,
comm=comm,
name=base_name,
distribution_name=distribution_name,
permutation_name=permutation_name)
bar = mesh.ExtrudedMesh(base, layers=nt, layer_height=2 * np.pi / nt, extrusion_type="uniform", periodic=True)
x, y = ufl.SpatialCoordinate(bar)
V = bar.coordinates.function_space()
coord = Function(V).interpolate(ufl.as_vector([x * ufl.cos(y), x * ufl.sin(y)]))
annulus = mesh.make_mesh_from_coordinates(coord.topological, name)
annulus.topology.name = mesh._generate_default_mesh_topology_name(name)
annulus._base_mesh = base
return annulus
[docs]
@PETSc.Log.EventDecorator()
def SolidTorusMesh(
R,
r,
nR=8,
refinement_level=0,
reorder=None,
distribution_parameters=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a solid toroidal mesh (with axis z) periodically extruding a disk mesh
:arg R: The major radius
:arg r: The minor radius
:kwarg nR: (optional), number of cells in the major direction (min 3)
:kwarg refinement_level: (optional), number of times the base disk mesh is refined.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if ``None``, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if ``None``, the name is automatically
generated.
"""
if nR < 3:
raise ValueError("Must have at least 3 cells in the major direction")
base_name = name + "_base"
unit = UnitDiskMesh(refinement_level=refinement_level,
reorder=reorder,
distribution_parameters=distribution_parameters,
comm=comm,
distribution_name=distribution_name,
permutation_name=permutation_name)
x, y = ufl.SpatialCoordinate(unit)
V = unit.coordinates.function_space()
coord = Function(V).interpolate(ufl.as_vector([r * x + R, r * y]))
disk = mesh.make_mesh_from_coordinates(coord.topological, base_name)
disk.topology.name = mesh._generate_default_mesh_topology_name(base_name)
disk.topology.topology_dm.setName(disk.topology.name)
bar = mesh.ExtrudedMesh(disk, layers=nR, layer_height=2 * np.pi / nR, extrusion_type="uniform", periodic=True)
x, y, z = ufl.SpatialCoordinate(bar)
V = bar.coordinates.function_space()
coord = Function(V).interpolate(ufl.as_vector([x * ufl.cos(z), x * ufl.sin(z), -y]))
torus = mesh.make_mesh_from_coordinates(coord.topological, name)
torus.topology.name = mesh._generate_default_mesh_topology_name(name)
torus._base_mesh = disk
return torus
[docs]
@PETSc.Log.EventDecorator()
def CylinderMesh(
nr,
nl,
radius=1,
depth=1,
longitudinal_direction="z",
quadrilateral=False,
reorder=None,
distribution_parameters=None,
diagonal=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generates a cylinder mesh.
:arg nr: number of cells the cylinder circumference should be
divided into (min 3)
:arg nl: number of cells along the longitudinal axis of the cylinder
:kwarg radius: (optional) radius of the cylinder to approximate.
:kwarg depth: (optional) depth of the cylinder to approximate.
:kwarg longitudinal_direction: (option) direction for the
longitudinal axis of the cylinder.
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg diagonal: (optional), one of ``"crossed"``, ``"left"``, ``"right"``.
Not valid for quad meshes.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
The boundary edges in this mesh are numbered as follows:
* 1: plane l == 0 (bottom)
* 2: plane l == depth (top)
"""
if nr < 3:
raise ValueError("CylinderMesh must have at least three cells")
if quadrilateral and diagonal is not None:
raise ValueError("Cannot specify slope of diagonal on quad meshes")
if not quadrilateral and diagonal is None:
diagonal = "left"
coord_xy = radius * np.column_stack(
(
np.cos(np.arange(nr) * (2 * np.pi / nr)),
np.sin(np.arange(nr) * (2 * np.pi / nr)),
)
)
coord_z = depth * np.linspace(0.0, 1.0, nl + 1).reshape(-1, 1)
vertices = np.asarray(
np.column_stack(
(np.tile(coord_xy, (nl + 1, 1)), np.tile(coord_z, (1, nr)).reshape(-1, 1))
),
dtype=np.double,
)
# intervals on circumference
ring_cells = np.column_stack(
(
np.arange(0, nr, dtype=np.int32),
np.roll(np.arange(0, nr, dtype=np.int32), -1),
)
)
# quads in the first layer
ring_cells = np.column_stack((ring_cells, np.roll(ring_cells, 1, axis=1) + nr))
if not quadrilateral and diagonal == "crossed":
dxy = np.pi / nr
Lxy = 2 * np.pi
extra_uv = np.linspace(dxy, Lxy - dxy, nr, dtype=np.double)
extra_xy = radius * np.column_stack((np.cos(extra_uv), np.sin(extra_uv)))
dz = 1 * 0.5 / nl
extra_z = depth * np.linspace(dz, 1 - dz, nl).reshape(-1, 1)
extras = np.asarray(
np.column_stack(
(np.tile(extra_xy, (nl, 1)), np.tile(extra_z, (1, nr)).reshape(-1, 1))
),
dtype=np.double,
)
origvertices = vertices
vertices = np.vstack([vertices, extras])
#
# 2-----3
# | \ / |
# | 4 |
# | / \ |
# 0-----1
offset = np.arange(nl, dtype=np.int32) * nr
origquads = np.row_stack(tuple(ring_cells + i for i in offset))
cells = np.zeros((origquads.shape[0] * 4, 3), dtype=np.int32)
cellidx = 0
newvertices = range(len(origvertices), len(origvertices) + len(extras))
for (origquad, extravertex) in zip(origquads, newvertices):
cells[cellidx + 0, :] = [origquad[0], origquad[1], extravertex]
cells[cellidx + 1, :] = [origquad[0], origquad[3], extravertex]
cells[cellidx + 2, :] = [origquad[3], origquad[2], extravertex]
cells[cellidx + 3, :] = [origquad[2], origquad[1], extravertex]
cellidx += 4
else:
offset = np.arange(nl, dtype=np.int32) * nr
cells = np.row_stack(tuple(ring_cells + i for i in offset))
if not quadrilateral:
if diagonal == "left":
idx = [0, 1, 3, 1, 2, 3]
elif diagonal == "right":
idx = [0, 1, 2, 0, 2, 3]
else:
raise ValueError("Unrecognised value for diagonal '%r'", diagonal)
# two cells per cell above...
cells = cells[:, idx].reshape(-1, 3)
if longitudinal_direction == "x":
rotation = np.asarray([[0, 0, 1], [0, 1, 0], [-1, 0, 0]], dtype=np.double)
vertices = np.dot(vertices, rotation.T)
elif longitudinal_direction == "y":
rotation = np.asarray([[1, 0, 0], [0, 0, 1], [0, -1, 0]], dtype=np.double)
vertices = np.dot(vertices, rotation.T)
elif longitudinal_direction != "z":
raise ValueError("Unknown longitudinal direction '%s'" % longitudinal_direction)
plex = mesh.plex_from_cell_list(
2, cells, vertices, comm, mesh._generate_default_mesh_topology_name(name)
)
plex.createLabel(dmcommon.FACE_SETS_LABEL)
plex.markBoundaryFaces("boundary_faces")
coords = plex.getCoordinates()
coord_sec = plex.getCoordinateSection()
if plex.getStratumSize("boundary_faces", 1) > 0:
boundary_faces = plex.getStratumIS("boundary_faces", 1).getIndices()
eps = depth / (2 * nl)
for face in boundary_faces:
face_coords = plex.vecGetClosure(coord_sec, coords, face)
# index of x/y/z coordinates of the face element
axis_ix = {"x": 0, "y": 1, "z": 2}
i = axis_ix[longitudinal_direction]
j = i + 3
if abs(face_coords[i]) < eps and abs(face_coords[j]) < eps:
# bottom of cylinder
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 1)
if abs(face_coords[i] - depth) < eps and abs(face_coords[j] - depth) < eps:
# top of cylinder
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, face, 2)
plex.removeLabel("boundary_faces")
return mesh.Mesh(
plex,
dim=3,
reorder=reorder,
distribution_parameters=distribution_parameters,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
comm=comm,
)
@PETSc.Log.EventDecorator()
def PartiallyPeriodicRectangleMesh(
nx,
ny,
Lx,
Ly,
direction="x",
quadrilateral=False,
reorder=None,
distribution_parameters=None,
diagonal=None,
comm=COMM_WORLD,
name=mesh.DEFAULT_MESH_NAME,
distribution_name=None,
permutation_name=None,
):
"""Generate a RectangleMesh that is periodic in the x or y direction.
:arg nx: The number of cells in the x direction
:arg ny: The number of cells in the y direction
:arg Lx: The extent in the x direction
:arg Ly: The extent in the y direction
:kwarg direction: The direction of the periodicity.
:kwarg quadrilateral: (optional), creates quadrilateral mesh.
:kwarg reorder: (optional), should the mesh be reordered
:kwarg distribution_parameters: options controlling mesh
distribution, see :func:`.Mesh` for details.
:kwarg diagonal: (optional), one of ``"crossed"``, ``"left"``, ``"right"``.
Not valid for quad meshes.
:kwarg comm: Optional communicator to build the mesh on.
:kwarg name: Optional name of the mesh.
:kwarg distribution_name: the name of parallel distribution used
when checkpointing; if `None`, the name is automatically
generated.
:kwarg permutation_name: the name of entity permutation (reordering) used
when checkpointing; if `None`, the name is automatically
generated.
If direction == "x" the boundary edges in this mesh are numbered as follows:
* 1: plane y == 0
* 2: plane y == Ly
If direction == "y" the boundary edges are:
* 1: plane x == 0
* 2: plane x == Lx
"""
if direction not in ("x", "y"):
raise ValueError("Unsupported periodic direction '%s'" % direction)
# handle x/y directions: na, La are for the periodic axis
na, nb = nx, ny
if direction == "y":
na, nb = ny, nx
if na < 3:
raise ValueError(
"2D periodic meshes with fewer than 3 cells in each direction are not currently supported"
)
m = CylinderMesh(
na,
nb,
1.0,
1.0,
longitudinal_direction="z",
quadrilateral=quadrilateral,
reorder=reorder_noop,
distribution_parameters=distribution_parameters_no_overlap,
diagonal=diagonal,
comm=comm,
name=name,
distribution_name=distribution_name,
permutation_name=permutation_name,
)
coord_family = "DQ" if quadrilateral else "DG"
cell = "quadrilateral" if quadrilateral else "triangle"
indicator = Function(FunctionSpace(m, coord_family, 0))
coord_fs = VectorFunctionSpace(
m, FiniteElement(coord_family, cell, 1, variant="equispaced"), dim=2
)
new_coordinates = Function(
coord_fs, name=mesh._generate_default_mesh_coordinates_name(name)
)
x, y, z = SpatialCoordinate(m)
eps = 1.e-14
indicator.interpolate(conditional(gt(real(y), 0), 0., 1.))
if direction == "x":
transform = as_tensor([[Lx, 0.], [0., Ly]])
else:
transform = as_tensor([[0., Lx], [Ly, 0]])
new_coordinates.interpolate(dot(
transform,
as_vector((
conditional(gt(real(x), real(1. - eps)), indicator, # Periodic break.
# Unwrap rest of circle.
atan2(real(-y), real(-x))/(2 * pi) + 0.5),
z
))
))
return _postprocess_periodic_mesh(new_coordinates,
comm,
distribution_parameters,
reorder,
name,
distribution_name,
permutation_name)
