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from warp.fem.types import ElementIndex, Coords
from warp.fem.polynomial import Polynomial, is_closed
from warp.fem.geometry import Hexmesh
from warp.fem import cache
from .topology import SpaceTopology, DiscontinuousSpaceTopologyMixin, forward_base_topology
from .basis_space import ShapeBasisSpace, TraceBasisSpace
from .shape import ShapeFunction, ConstantShapeFunction
from .shape import (
CubeTripolynomialShapeFunctions,
CubeSerendipityShapeFunctions,
CubeNonConformingPolynomialShapeFunctions,
)
from warp.fem.geometry.hexmesh import (
EDGE_VERTEX_INDICES,
FACE_ORIENTATION,
FACE_TRANSLATION,
)
_FACE_ORIENTATION_I = wp.constant(wp.mat(shape=(16, 2), dtype=int)(FACE_ORIENTATION))
_FACE_TRANSLATION_I = wp.constant(wp.mat(shape=(4, 2), dtype=int)(FACE_TRANSLATION))
_CUBE_VERTEX_INDICES = wp.constant(wp.vec(length=8, dtype=int)([0, 4, 3, 7, 1, 5, 2, 6]))
@wp.struct
class HexmeshTopologyArg:
hex_edge_indices: wp.array2d(dtype=int)
hex_face_indices: wp.array2d(dtype=wp.vec2i)
vertex_count: int
edge_count: int
face_count: int
class HexmeshSpaceTopology(SpaceTopology):
TopologyArg = HexmeshTopologyArg
def __init__(
self,
mesh: Hexmesh,
shape: ShapeFunction,
need_hex_edge_indices: bool = True,
need_hex_face_indices: bool = True,
):
super().__init__(mesh, shape.NODES_PER_ELEMENT)
self._mesh = mesh
self._shape = shape
if need_hex_edge_indices:
self._hex_edge_indices = self._mesh.hex_edge_indices
self._edge_count = self._mesh.edge_count()
else:
self._hex_edge_indices = wp.empty(shape=(0, 0), dtype=int)
self._edge_count = 0
if need_hex_face_indices:
self._compute_hex_face_indices()
else:
self._hex_face_indices = wp.empty(shape=(0, 0), dtype=wp.vec2i)
self._compute_hex_face_indices()
@cache.cached_arg_value
def topo_arg_value(self, device):
arg = HexmeshTopologyArg()
arg.hex_edge_indices = self._hex_edge_indices.to(device)
arg.hex_face_indices = self._hex_face_indices.to(device)
arg.vertex_count = self._mesh.vertex_count()
arg.face_count = self._mesh.side_count()
arg.edge_count = self._edge_count
return arg
def _compute_hex_face_indices(self):
self._hex_face_indices = wp.empty(
dtype=wp.vec2i, device=self._mesh.hex_vertex_indices.device, shape=(self._mesh.cell_count(), 6)
)
wp.launch(
kernel=HexmeshSpaceTopology._compute_hex_face_indices_kernel,
dim=self._mesh.side_count(),
device=self._mesh.hex_vertex_indices.device,
inputs=[
self._mesh.face_hex_indices,
self._mesh._face_hex_face_orientation,
self._hex_face_indices,
],
)
@wp.kernel
def _compute_hex_face_indices_kernel(
face_hex_indices: wp.array(dtype=wp.vec2i),
face_hex_face_ori: wp.array(dtype=wp.vec4i),
hex_face_indices: wp.array2d(dtype=wp.vec2i),
):
f = wp.tid()
hx0 = face_hex_indices[f][0]
local_face_0 = face_hex_face_ori[f][0]
ori_0 = face_hex_face_ori[f][1]
hex_face_indices[hx0, local_face_0] = wp.vec2i(f, ori_0)
hx1 = face_hex_indices[f][1]
local_face_1 = face_hex_face_ori[f][2]
ori_1 = face_hex_face_ori[f][3]
hex_face_indices[hx1, local_face_1] = wp.vec2i(f, ori_1)
class HexmeshDiscontinuousSpaceTopology(
DiscontinuousSpaceTopologyMixin,
SpaceTopology,
):
def __init__(self, mesh: Hexmesh, shape: ShapeFunction):
super().__init__(mesh, shape.NODES_PER_ELEMENT)
class HexmeshBasisSpace(ShapeBasisSpace):
def __init__(self, topology: HexmeshSpaceTopology, shape: ShapeFunction):
super().__init__(topology, shape)
self._mesh: Hexmesh = topology.geometry
class HexmeshPiecewiseConstantBasis(HexmeshBasisSpace):
def __init__(self, mesh: Hexmesh):
shape = ConstantShapeFunction(mesh.reference_cell(), space_dimension=3)
topology = HexmeshDiscontinuousSpaceTopology(mesh, shape)
super().__init__(shape=shape, topology=topology)
class Trace(TraceBasisSpace):
@wp.func
def _node_coords_in_element(
side_arg: Hexmesh.SideArg,
basis_arg: HexmeshBasisSpace.BasisArg,
element_index: ElementIndex,
node_index_in_element: int,
):
return Coords(0.5, 0.5, 0.0)
def make_node_coords_in_element(self):
return self._node_coords_in_element
def trace(self):
return HexmeshPiecewiseConstantBasis.Trace(self)
class HexmeshTripolynomialSpaceTopology(HexmeshSpaceTopology):
def __init__(self, mesh: Hexmesh, shape: CubeTripolynomialShapeFunctions):
super().__init__(mesh, shape, need_hex_edge_indices=shape.ORDER >= 2, need_hex_face_indices=shape.ORDER >= 2)
self.element_node_index = self._make_element_node_index()
def node_count(self) -> int:
ORDER = self._shape.ORDER
INTERIOR_NODES_PER_EDGE = max(0, ORDER - 1)
INTERIOR_NODES_PER_FACE = INTERIOR_NODES_PER_EDGE**2
INTERIOR_NODES_PER_CELL = INTERIOR_NODES_PER_EDGE**3
return (
self._mesh.vertex_count()
+ self._mesh.edge_count() * INTERIOR_NODES_PER_EDGE
+ self._mesh.side_count() * INTERIOR_NODES_PER_FACE
+ self._mesh.cell_count() * INTERIOR_NODES_PER_CELL
)
@wp.func
def _rotate_face_index(type_index: int, ori: int, size: int):
i = type_index // size
j = type_index - i * size
coords = wp.vec2i(i, j)
fv = ori // 2
rot_i = wp.dot(_FACE_ORIENTATION_I[2 * ori], coords) + _FACE_TRANSLATION_I[fv, 0]
rot_j = wp.dot(_FACE_ORIENTATION_I[2 * ori + 1], coords) + _FACE_TRANSLATION_I[fv, 1]
return rot_i * size + rot_j
def _make_element_node_index(self):
ORDER = self._shape.ORDER
INTERIOR_NODES_PER_EDGE = wp.constant(max(0, ORDER - 1))
INTERIOR_NODES_PER_FACE = wp.constant(INTERIOR_NODES_PER_EDGE**2)
INTERIOR_NODES_PER_CELL = wp.constant(INTERIOR_NODES_PER_EDGE**3)
@cache.dynamic_func(suffix=self.name)
def element_node_index(
geo_arg: Hexmesh.CellArg,
topo_arg: HexmeshTopologyArg,
element_index: ElementIndex,
node_index_in_elt: int,
):
node_type, type_instance, type_index = self._shape.node_type_and_type_index(node_index_in_elt)
if node_type == CubeTripolynomialShapeFunctions.VERTEX:
return geo_arg.hex_vertex_indices[element_index, _CUBE_VERTEX_INDICES[type_instance]]
offset = topo_arg.vertex_count
if node_type == CubeTripolynomialShapeFunctions.EDGE:
edge_index = topo_arg.hex_edge_indices[element_index, type_instance]
v0 = geo_arg.hex_vertex_indices[element_index, EDGE_VERTEX_INDICES[type_instance, 0]]
v1 = geo_arg.hex_vertex_indices[element_index, EDGE_VERTEX_INDICES[type_instance, 1]]
if v0 > v1:
type_index = ORDER - 1 - type_index
return offset + INTERIOR_NODES_PER_EDGE * edge_index + type_index
offset += INTERIOR_NODES_PER_EDGE * topo_arg.edge_count
if node_type == CubeTripolynomialShapeFunctions.FACE:
face_index_and_ori = topo_arg.hex_face_indices[element_index, type_instance]
face_index = face_index_and_ori[0]
face_orientation = face_index_and_ori[1]
type_index = HexmeshTripolynomialSpaceTopology._rotate_face_index(
type_index, face_orientation, ORDER - 1
)
return offset + INTERIOR_NODES_PER_FACE * face_index + type_index
offset += INTERIOR_NODES_PER_FACE * topo_arg.face_count
return offset + INTERIOR_NODES_PER_CELL * element_index + type_index
return element_node_index
class HexmeshTripolynomialBasisSpace(HexmeshBasisSpace):
def __init__(
self,
mesh: Hexmesh,
degree: int,
family: Polynomial,
):
if family is None:
family = Polynomial.LOBATTO_GAUSS_LEGENDRE
if not is_closed(family):
raise ValueError("A closed polynomial family is required to define a continuous function space")
shape = CubeTripolynomialShapeFunctions(degree, family=family)
topology = forward_base_topology(HexmeshTripolynomialSpaceTopology, mesh, shape)
super().__init__(topology, shape)
class HexmeshDGTripolynomialBasisSpace(HexmeshBasisSpace):
def __init__(
self,
mesh: Hexmesh,
degree: int,
family: Polynomial,
):
if family is None:
family = Polynomial.LOBATTO_GAUSS_LEGENDRE
shape = CubeTripolynomialShapeFunctions(degree, family=family)
topology = HexmeshDiscontinuousSpaceTopology(mesh, shape)
super().__init__(topology, shape)
class HexmeshSerendipitySpaceTopology(HexmeshSpaceTopology):
def __init__(self, grid: Hexmesh, shape: CubeSerendipityShapeFunctions):
super().__init__(grid, shape, need_hex_edge_indices=True, need_hex_face_indices=False)
self.element_node_index = self._make_element_node_index()
def node_count(self) -> int:
return self.geometry.vertex_count() + (self._shape.ORDER - 1) * self.geometry.edge_count()
def _make_element_node_index(self):
ORDER = self._shape.ORDER
@cache.dynamic_func(suffix=self.name)
def element_node_index(
cell_arg: Hexmesh.CellArg,
topo_arg: HexmeshSpaceTopology.TopologyArg,
element_index: ElementIndex,
node_index_in_elt: int,
):
node_type, type_index = self._shape.node_type_and_type_index(node_index_in_elt)
if node_type == CubeSerendipityShapeFunctions.VERTEX:
return cell_arg.hex_vertex_indices[element_index, _CUBE_VERTEX_INDICES[type_index]]
type_instance, index_in_edge = CubeSerendipityShapeFunctions._cube_edge_index(node_type, type_index)
edge_index = topo_arg.hex_edge_indices[element_index, type_instance]
v0 = cell_arg.hex_vertex_indices[element_index, EDGE_VERTEX_INDICES[type_instance, 0]]
v1 = cell_arg.hex_vertex_indices[element_index, EDGE_VERTEX_INDICES[type_instance, 1]]
if v0 > v1:
index_in_edge = ORDER - 1 - index_in_edge
return topo_arg.vertex_count + (ORDER - 1) * edge_index + index_in_edge
return element_node_index
class HexmeshSerendipityBasisSpace(HexmeshBasisSpace):
def __init__(
self,
mesh: Hexmesh,
degree: int,
family: Polynomial,
):
if family is None:
family = Polynomial.LOBATTO_GAUSS_LEGENDRE
shape = CubeSerendipityShapeFunctions(degree, family=family)
topology = forward_base_topology(HexmeshSerendipitySpaceTopology, mesh, shape=shape)
super().__init__(topology=topology, shape=shape)
class HexmeshDGSerendipityBasisSpace(HexmeshBasisSpace):
def __init__(
self,
mesh: Hexmesh,
degree: int,
family: Polynomial,
):
if family is None:
family = Polynomial.LOBATTO_GAUSS_LEGENDRE
shape = CubeSerendipityShapeFunctions(degree, family=family)
topology = HexmeshDiscontinuousSpaceTopology(mesh, shape=shape)
super().__init__(topology=topology, shape=shape)
class HexmeshPolynomialBasisSpace(HexmeshBasisSpace):
def __init__(
self,
mesh: Hexmesh,
degree: int,
):
shape = CubeNonConformingPolynomialShapeFunctions(degree)
topology = HexmeshDiscontinuousSpaceTopology(mesh, shape)
super().__init__(topology, shape)
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