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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 | import warp as wp
from warp.fem.types import ElementIndex, Coords
from warp.fem.geometry import Trimesh2D
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 Triangle2DPolynomialShapeFunctions, Triangle2DNonConformingPolynomialShapeFunctions
@wp.struct
class Trimesh2DTopologyArg:
edge_vertex_indices: wp.array(dtype=wp.vec2i)
tri_edge_indices: wp.array2d(dtype=int)
vertex_count: int
edge_count: int
class Trimesh2DSpaceTopology(SpaceTopology):
TopologyArg = Trimesh2DTopologyArg
def __init__(self, mesh: Trimesh2D, shape: ShapeFunction):
super().__init__(mesh, shape.NODES_PER_ELEMENT)
self._mesh = mesh
self._shape = shape
self._compute_tri_edge_indices()
@cache.cached_arg_value
def topo_arg_value(self, device):
arg = Trimesh2DTopologyArg()
arg.tri_edge_indices = self._tri_edge_indices.to(device)
arg.edge_vertex_indices = self._mesh.edge_vertex_indices.to(device)
arg.vertex_count = self._mesh.vertex_count()
arg.edge_count = self._mesh.side_count()
return arg
def _compute_tri_edge_indices(self):
self._tri_edge_indices = wp.empty(
dtype=int, device=self._mesh.tri_vertex_indices.device, shape=(self._mesh.cell_count(), 3)
)
wp.launch(
kernel=Trimesh2DSpaceTopology._compute_tri_edge_indices_kernel,
dim=self._mesh.edge_tri_indices.shape,
device=self._mesh.tri_vertex_indices.device,
inputs=[
self._mesh.edge_tri_indices,
self._mesh.edge_vertex_indices,
self._mesh.tri_vertex_indices,
self._tri_edge_indices,
],
)
@wp.func
def _find_edge_index_in_tri(
edge_vtx: wp.vec2i,
tri_vtx: wp.vec3i,
):
for k in range(2):
if (edge_vtx[0] == tri_vtx[k] and edge_vtx[1] == tri_vtx[k + 1]) or (
edge_vtx[1] == tri_vtx[k] and edge_vtx[0] == tri_vtx[k + 1]
):
return k
return 2
@wp.kernel
def _compute_tri_edge_indices_kernel(
edge_tri_indices: wp.array(dtype=wp.vec2i),
edge_vertex_indices: wp.array(dtype=wp.vec2i),
tri_vertex_indices: wp.array2d(dtype=int),
tri_edge_indices: wp.array2d(dtype=int),
):
e = wp.tid()
edge_vtx = edge_vertex_indices[e]
edge_tris = edge_tri_indices[e]
t0 = edge_tris[0]
t0_vtx = wp.vec3i(tri_vertex_indices[t0, 0], tri_vertex_indices[t0, 1], tri_vertex_indices[t0, 2])
t0_edge = Trimesh2DSpaceTopology._find_edge_index_in_tri(edge_vtx, t0_vtx)
tri_edge_indices[t0, t0_edge] = e
t1 = edge_tris[1]
if t1 != t0:
t1_vtx = wp.vec3i(tri_vertex_indices[t1, 0], tri_vertex_indices[t1, 1], tri_vertex_indices[t1, 2])
t1_edge = Trimesh2DSpaceTopology._find_edge_index_in_tri(edge_vtx, t1_vtx)
tri_edge_indices[t1, t1_edge] = e
class Trimesh2DDiscontinuousSpaceTopology(
DiscontinuousSpaceTopologyMixin,
SpaceTopology,
):
def __init__(self, mesh: Trimesh2D, shape: ShapeFunction):
super().__init__(mesh, shape.NODES_PER_ELEMENT)
class Trimesh2DBasisSpace(ShapeBasisSpace):
def __init__(self, topology: Trimesh2DSpaceTopology, shape: ShapeFunction):
super().__init__(topology, shape)
self._mesh: Trimesh2D = topology.geometry
class Trimesh2DPiecewiseConstantBasis(Trimesh2DBasisSpace):
def __init__(self, mesh: Trimesh2D):
shape = ConstantShapeFunction(mesh.reference_cell(), space_dimension=2)
topology = Trimesh2DDiscontinuousSpaceTopology(mesh, shape)
super().__init__(shape=shape, topology=topology)
class Trace(TraceBasisSpace):
@wp.func
def _node_coords_in_element(
side_arg: Trimesh2D.SideArg,
basis_arg: Trimesh2DBasisSpace.BasisArg,
element_index: ElementIndex,
node_index_in_element: int,
):
return Coords(0.5, 0.0, 0.0)
def make_node_coords_in_element(self):
return self._node_coords_in_element
def trace(self):
return Trimesh2DPiecewiseConstantBasis.Trace(self)
class Trimesh2DPolynomialSpaceTopology(Trimesh2DSpaceTopology):
def __init__(self, mesh: Trimesh2D, shape: Triangle2DPolynomialShapeFunctions):
super().__init__(mesh, shape)
self.element_node_index = self._make_element_node_index()
def node_count(self) -> int:
INTERIOR_NODES_PER_SIDE = max(0, self._shape.ORDER - 1)
INTERIOR_NODES_PER_CELL = max(0, self._shape.ORDER - 2) * max(0, self._shape.ORDER - 1) // 2
return (
self._mesh.vertex_count()
+ self._mesh.side_count() * INTERIOR_NODES_PER_SIDE
+ self._mesh.cell_count() * INTERIOR_NODES_PER_CELL
)
def _make_element_node_index(self):
INTERIOR_NODES_PER_SIDE = wp.constant(max(0, self._shape.ORDER - 1))
INTERIOR_NODES_PER_CELL = wp.constant(max(0, self._shape.ORDER - 2) * max(0, self._shape.ORDER - 1) // 2)
@cache.dynamic_func(suffix=self.name)
def element_node_index(
geo_arg: Trimesh2D.CellArg,
topo_arg: Trimesh2DTopologyArg,
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 == Triangle2DPolynomialShapeFunctions.VERTEX:
return geo_arg.tri_vertex_indices[element_index][type_index]
global_offset = topo_arg.vertex_count
if node_type == Triangle2DPolynomialShapeFunctions.EDGE:
edge = type_index // INTERIOR_NODES_PER_SIDE
edge_node = type_index - INTERIOR_NODES_PER_SIDE * edge
global_edge_index = topo_arg.tri_edge_indices[element_index][edge]
if (
topo_arg.edge_vertex_indices[global_edge_index][0]
!= geo_arg.tri_vertex_indices[element_index][edge]
):
edge_node = INTERIOR_NODES_PER_SIDE - 1 - edge_node
return global_offset + INTERIOR_NODES_PER_SIDE * global_edge_index + edge_node
global_offset += INTERIOR_NODES_PER_SIDE * topo_arg.edge_count
return global_offset + INTERIOR_NODES_PER_CELL * element_index + type_index
return element_node_index
class Trimesh2DPolynomialBasisSpace(Trimesh2DBasisSpace):
def __init__(
self,
mesh: Trimesh2D,
degree: int,
):
shape = Triangle2DPolynomialShapeFunctions(degree)
topology = forward_base_topology(Trimesh2DPolynomialSpaceTopology, mesh, shape)
super().__init__(topology, shape)
class Trimesh2DDGPolynomialBasisSpace(Trimesh2DBasisSpace):
def __init__(
self,
mesh: Trimesh2D,
degree: int,
):
shape = Triangle2DPolynomialShapeFunctions(degree)
topology = Trimesh2DDiscontinuousSpaceTopology(mesh, shape)
super().__init__(topology, shape)
class Trimesh2DNonConformingPolynomialBasisSpace(Trimesh2DBasisSpace):
def __init__(
self,
mesh: Trimesh2D,
degree: int,
):
shape = Triangle2DNonConformingPolynomialShapeFunctions(degree)
topology = Trimesh2DDiscontinuousSpaceTopology(mesh, shape)
super().__init__(topology, shape)
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