Spaces:
Sleeping
Sleeping
File size: 10,426 Bytes
66c9c8a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 | import warp as wp
from warp.fem.types import ElementIndex, Coords
from warp.fem.geometry import Tetmesh
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 TetrahedronPolynomialShapeFunctions, TetrahedronNonConformingPolynomialShapeFunctions
@wp.struct
class TetmeshTopologyArg:
tet_edge_indices: wp.array2d(dtype=int)
tet_face_indices: wp.array2d(dtype=int)
face_vertex_indices: wp.array(dtype=wp.vec3i)
vertex_count: int
edge_count: int
face_count: int
class TetmeshSpaceTopology(SpaceTopology):
TopologyArg = TetmeshTopologyArg
def __init__(
self,
mesh: Tetmesh,
shape: ShapeFunction,
need_tet_edge_indices: bool = True,
need_tet_face_indices: bool = True,
):
super().__init__(mesh, shape.NODES_PER_ELEMENT)
self._mesh = mesh
self._shape = shape
if need_tet_edge_indices:
self._tet_edge_indices = self._mesh.tet_edge_indices
self._edge_count = self._mesh.edge_count()
else:
self._tet_edge_indices = wp.empty(shape=(0, 0), dtype=int)
self._edge_count = 0
if need_tet_face_indices:
self._compute_tet_face_indices()
else:
self._tet_face_indices = wp.empty(shape=(0, 0), dtype=int)
@cache.cached_arg_value
def topo_arg_value(self, device):
arg = TetmeshTopologyArg()
arg.tet_face_indices = self._tet_face_indices.to(device)
arg.tet_edge_indices = self._tet_edge_indices.to(device)
arg.face_vertex_indices = self._mesh.face_vertex_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_tet_face_indices(self):
self._tet_face_indices = wp.empty(
dtype=int, device=self._mesh.tet_vertex_indices.device, shape=(self._mesh.cell_count(), 4)
)
wp.launch(
kernel=TetmeshSpaceTopology._compute_tet_face_indices_kernel,
dim=self._mesh._face_tet_indices.shape,
device=self._mesh.tet_vertex_indices.device,
inputs=[
self._mesh.face_tet_indices,
self._mesh.face_vertex_indices,
self._mesh.tet_vertex_indices,
self._tet_face_indices,
],
)
@wp.func
def _find_face_index_in_tet(
face_vtx: wp.vec3i,
tet_vtx: wp.vec4i,
):
for k in range(3):
tvk = wp.vec3i(tet_vtx[k], tet_vtx[(k + 1) % 4], tet_vtx[(k + 2) % 4])
# Use fact that face always start with min vertex
min_t = wp.min(tvk)
max_t = wp.max(tvk)
mid_t = tvk[0] + tvk[1] + tvk[2] - min_t - max_t
if min_t == face_vtx[0] and (
(face_vtx[2] == max_t and face_vtx[1] == mid_t) or (face_vtx[1] == max_t and face_vtx[2] == mid_t)
):
return k
return 3
@wp.kernel
def _compute_tet_face_indices_kernel(
face_tet_indices: wp.array(dtype=wp.vec2i),
face_vertex_indices: wp.array(dtype=wp.vec3i),
tet_vertex_indices: wp.array2d(dtype=int),
tet_face_indices: wp.array2d(dtype=int),
):
e = wp.tid()
face_vtx = face_vertex_indices[e]
face_tets = face_tet_indices[e]
t0 = face_tets[0]
t0_vtx = wp.vec4i(
tet_vertex_indices[t0, 0], tet_vertex_indices[t0, 1], tet_vertex_indices[t0, 2], tet_vertex_indices[t0, 3]
)
t0_face = TetmeshSpaceTopology._find_face_index_in_tet(face_vtx, t0_vtx)
tet_face_indices[t0, t0_face] = e
t1 = face_tets[1]
if t1 != t0:
t1_vtx = wp.vec4i(
tet_vertex_indices[t1, 0],
tet_vertex_indices[t1, 1],
tet_vertex_indices[t1, 2],
tet_vertex_indices[t1, 3],
)
t1_face = TetmeshSpaceTopology._find_face_index_in_tet(face_vtx, t1_vtx)
tet_face_indices[t1, t1_face] = e
class TetmeshDiscontinuousSpaceTopology(
DiscontinuousSpaceTopologyMixin,
SpaceTopology,
):
def __init__(self, mesh: Tetmesh, shape: ShapeFunction):
super().__init__(mesh, shape.NODES_PER_ELEMENT)
class TetmeshBasisSpace(ShapeBasisSpace):
def __init__(self, topology: TetmeshSpaceTopology, shape: ShapeFunction):
super().__init__(topology, shape)
self._mesh: Tetmesh = topology.geometry
class TetmeshPiecewiseConstantBasis(TetmeshBasisSpace):
def __init__(self, mesh: Tetmesh):
shape = ConstantShapeFunction(mesh.reference_cell(), space_dimension=3)
topology = TetmeshDiscontinuousSpaceTopology(mesh, shape)
super().__init__(shape=shape, topology=topology)
class Trace(TraceBasisSpace):
@wp.func
def _node_coords_in_element(
side_arg: Tetmesh.SideArg,
basis_arg: TetmeshBasisSpace.BasisArg,
element_index: ElementIndex,
node_index_in_element: int,
):
return Coords(1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0)
def make_node_coords_in_element(self):
return self._node_coords_in_element
def trace(self):
return TetmeshPiecewiseConstantBasis.Trace(self)
class TetmeshPolynomialSpaceTopology(TetmeshSpaceTopology):
def __init__(self, mesh: Tetmesh, shape: TetrahedronPolynomialShapeFunctions):
super().__init__(mesh, shape, need_tet_edge_indices=shape.ORDER >= 2, need_tet_face_indices=shape.ORDER >= 3)
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 = max(0, ORDER - 2) * max(0, ORDER - 1) // 2
INTERIOR_NODES_PER_CELL = max(0, ORDER - 3) * max(0, ORDER - 2) * max(0, ORDER - 1) // 6
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
)
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(max(0, ORDER - 2) * max(0, ORDER - 1) // 2)
INTERIOR_NODES_PER_CELL = wp.constant(max(0, ORDER - 3) * max(0, ORDER - 2) * max(0, ORDER - 1) // 6)
@cache.dynamic_func(suffix=self.name)
def element_node_index(
geo_arg: Tetmesh.CellArg,
topo_arg: TetmeshTopologyArg,
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 == TetrahedronPolynomialShapeFunctions.VERTEX:
return geo_arg.tet_vertex_indices[element_index][type_index]
global_offset = topo_arg.vertex_count
if node_type == TetrahedronPolynomialShapeFunctions.EDGE:
edge = type_index // INTERIOR_NODES_PER_EDGE
edge_node = type_index - INTERIOR_NODES_PER_EDGE * edge
global_edge_index = topo_arg.tet_edge_indices[element_index][edge]
# Test if we need to swap edge direction
if INTERIOR_NODES_PER_EDGE > 1:
if edge < 3:
c1 = edge
c2 = (edge + 1) % 3
else:
c1 = edge - 3
c2 = 3
if geo_arg.tet_vertex_indices[element_index][c1] > geo_arg.tet_vertex_indices[element_index][c2]:
edge_node = INTERIOR_NODES_PER_EDGE - 1 - edge_node
return global_offset + INTERIOR_NODES_PER_EDGE * global_edge_index + edge_node
global_offset += INTERIOR_NODES_PER_EDGE * topo_arg.edge_count
if node_type == TetrahedronPolynomialShapeFunctions.FACE:
face = type_index // INTERIOR_NODES_PER_FACE
face_node = type_index - INTERIOR_NODES_PER_FACE * face
global_face_index = topo_arg.tet_face_indices[element_index][face]
if INTERIOR_NODES_PER_FACE == 3:
# Hard code for P4 case, 3 nodes per face
# Higher orders would require rotating triangle coordinates, this is not supported yet
vidx = geo_arg.tet_vertex_indices[element_index][(face + face_node) % 4]
fvi = topo_arg.face_vertex_indices[global_face_index]
if vidx == fvi[0]:
face_node = 0
elif vidx == fvi[1]:
face_node = 1
else:
face_node = 2
return global_offset + INTERIOR_NODES_PER_FACE * global_face_index + face_node
global_offset += INTERIOR_NODES_PER_FACE * topo_arg.face_count
return global_offset + INTERIOR_NODES_PER_CELL * element_index + type_index
return element_node_index
class TetmeshPolynomialBasisSpace(TetmeshBasisSpace):
def __init__(
self,
mesh: Tetmesh,
degree: int,
):
shape = TetrahedronPolynomialShapeFunctions(degree)
topology = forward_base_topology(TetmeshPolynomialSpaceTopology, mesh, shape)
super().__init__(topology, shape)
class TetmeshDGPolynomialBasisSpace(TetmeshBasisSpace):
def __init__(
self,
mesh: Tetmesh,
degree: int,
):
shape = TetrahedronPolynomialShapeFunctions(degree)
topology = TetmeshDiscontinuousSpaceTopology(mesh, shape)
super().__init__(topology, shape)
class TetmeshNonConformingPolynomialBasisSpace(TetmeshBasisSpace):
def __init__(
self,
mesh: Tetmesh,
degree: int,
):
shape = TetrahedronNonConformingPolynomialShapeFunctions(degree)
topology = TetmeshDiscontinuousSpaceTopology(mesh, shape)
super().__init__(topology, shape)
|