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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 | import warp as wp
import numpy as np
from warp.fem.types import ElementIndex, Coords
from warp.fem.polynomial import Polynomial, is_closed
from warp.fem.geometry import Grid2D
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 (
SquareBipolynomialShapeFunctions,
SquareSerendipityShapeFunctions,
SquareNonConformingPolynomialShapeFunctions,
)
class Grid2DSpaceTopology(SpaceTopology):
def __init__(self, grid: Grid2D, shape: ShapeFunction):
super().__init__(grid, shape.NODES_PER_ELEMENT)
self._shape = shape
@wp.func
def _vertex_coords(vidx_in_cell: int):
x = vidx_in_cell // 2
y = vidx_in_cell - 2 * x
return wp.vec2i(x, y)
@wp.func
def _vertex_index(cell_arg: Grid2D.CellArg, cell_index: ElementIndex, vidx_in_cell: int):
res = cell_arg.res
x_stride = res[1] + 1
corner = Grid2D.get_cell(res, cell_index) + Grid2DSpaceTopology._vertex_coords(vidx_in_cell)
return Grid2D._from_2d_index(x_stride, corner)
class Grid2DDiscontinuousSpaceTopology(
DiscontinuousSpaceTopologyMixin,
Grid2DSpaceTopology,
):
pass
class Grid2DBasisSpace(ShapeBasisSpace):
def __init__(self, topology: Grid2DSpaceTopology, shape: ShapeFunction):
super().__init__(topology, shape)
self._grid: Grid2D = topology.geometry
class GridPiecewiseConstantBasis(Grid2DBasisSpace):
def __init__(self, grid: Grid2D):
shape = ConstantShapeFunction(grid.reference_cell(), space_dimension=2)
topology = Grid2DDiscontinuousSpaceTopology(grid, shape)
super().__init__(shape=shape, topology=topology)
if isinstance(grid, Grid2D):
self.node_grid = self._node_grid
def _node_grid(self):
res = self._grid.res
X = (np.arange(0, res[0], dtype=float) + 0.5) * self._grid.cell_size[0] + self._grid.origin[0]
Y = (np.arange(0, res[1], dtype=float) + 0.5) * self._grid.cell_size[1] + self._grid.origin[1]
return np.meshgrid(X, Y, indexing="ij")
class Trace(TraceBasisSpace):
@wp.func
def _node_coords_in_element(
side_arg: Grid2D.SideArg,
basis_arg: Grid2DBasisSpace.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 GridPiecewiseConstantBasis.Trace(self)
class GridBipolynomialSpaceTopology(Grid2DSpaceTopology):
def __init__(self, grid: Grid2D, shape: SquareBipolynomialShapeFunctions):
super().__init__(grid, shape)
self.element_node_index = self._make_element_node_index()
def node_count(self) -> int:
return (self.geometry.res[0] * self._shape.ORDER + 1) * (self.geometry.res[1] * self._shape.ORDER + 1)
def _make_element_node_index(self):
ORDER = self._shape.ORDER
@cache.dynamic_func(suffix=self.name)
def element_node_index(
cell_arg: Grid2D.CellArg,
topo_arg: Grid2DSpaceTopology.TopologyArg,
element_index: ElementIndex,
node_index_in_elt: int,
):
res = cell_arg.res
cell = Grid2D.get_cell(res, element_index)
node_i = node_index_in_elt // (ORDER + 1)
node_j = node_index_in_elt - (ORDER + 1) * node_i
node_x = ORDER * cell[0] + node_i
node_y = ORDER * cell[1] + node_j
node_pitch = (res[1] * ORDER) + 1
node_index = node_pitch * node_x + node_y
return node_index
return element_node_index
class GridBipolynomialBasisSpace(Grid2DBasisSpace):
def __init__(
self,
grid: Grid2D,
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 = SquareBipolynomialShapeFunctions(degree, family=family)
topology = forward_base_topology(GridBipolynomialSpaceTopology, grid, shape)
super().__init__(topology, shape)
if isinstance(grid, Grid2D):
self.node_grid = self._node_grid
def _node_grid(self):
res = self._grid.res
cell_coords = np.array(self._shape.LOBATTO_COORDS)[:-1]
grid_coords_x = np.repeat(np.arange(0, res[0], dtype=float), len(cell_coords)) + np.tile(
cell_coords, reps=res[0]
)
grid_coords_x = np.append(grid_coords_x, res[0])
X = grid_coords_x * self._grid.cell_size[0] + self._grid.origin[0]
grid_coords_y = np.repeat(np.arange(0, res[1], dtype=float), len(cell_coords)) + np.tile(
cell_coords, reps=res[1]
)
grid_coords_y = np.append(grid_coords_y, res[1])
Y = grid_coords_y * self._grid.cell_size[1] + self._grid.origin[1]
return np.meshgrid(X, Y, indexing="ij")
class GridDGBipolynomialBasisSpace(Grid2DBasisSpace):
def __init__(
self,
grid: Grid2D,
degree: int,
family: Polynomial,
):
if family is None:
family = Polynomial.LOBATTO_GAUSS_LEGENDRE
shape = SquareBipolynomialShapeFunctions(degree, family=family)
topology = Grid2DDiscontinuousSpaceTopology(grid, shape)
super().__init__(shape=shape, topology=topology)
class GridSerendipitySpaceTopology(Grid2DSpaceTopology):
def __init__(self, grid: Grid2D, shape: SquareSerendipityShapeFunctions):
super().__init__(grid, shape)
self.element_node_index = self._make_element_node_index()
TopologyArg = Grid2D.SideArg
def topo_arg_value(self, device):
return self.geometry.side_arg_value(device)
def node_count(self) -> int:
return self.geometry.vertex_count() + (self._shape.ORDER - 1) * self.geometry.side_count()
def _make_element_node_index(self):
ORDER = self._shape.ORDER
@cache.dynamic_func(suffix=self.name)
def element_node_index(
cell_arg: Grid2D.CellArg,
topo_arg: Grid2D.SideArg,
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 == SquareSerendipityShapeFunctions.VERTEX:
return Grid2DSpaceTopology._vertex_index(cell_arg, element_index, type_index)
side_offset, index_in_side = SquareSerendipityShapeFunctions.side_offset_and_index(type_index)
axis = 1 - (node_type - SquareSerendipityShapeFunctions.EDGE_X)
cell = Grid2D.get_cell(cell_arg.res, element_index)
origin = wp.vec2i(cell[Grid2D.ROTATION[axis, 0]] + side_offset, cell[Grid2D.ROTATION[axis, 1]])
side = Grid2D.Side(axis, origin)
side_index = Grid2D.side_index(topo_arg, side)
res = cell_arg.res
vertex_count = (res[0] + 1) * (res[1] + 1)
return vertex_count + (ORDER - 1) * side_index + index_in_side
return element_node_index
class GridSerendipityBasisSpace(Grid2DBasisSpace):
def __init__(
self,
grid: Grid2D,
degree: int,
family: Polynomial,
):
if family is None:
family = Polynomial.LOBATTO_GAUSS_LEGENDRE
shape = SquareSerendipityShapeFunctions(degree, family=family)
topology = forward_base_topology(GridSerendipitySpaceTopology, grid, shape=shape)
super().__init__(topology=topology, shape=shape)
class GridDGSerendipityBasisSpace(Grid2DBasisSpace):
def __init__(
self,
grid: Grid2D,
degree: int,
family: Polynomial,
):
if family is None:
family = Polynomial.LOBATTO_GAUSS_LEGENDRE
shape = SquareSerendipityShapeFunctions(degree, family=family)
topology = Grid2DDiscontinuousSpaceTopology(grid, shape=shape)
super().__init__(topology=topology, shape=shape)
class GridDGPolynomialBasisSpace(Grid2DBasisSpace):
def __init__(
self,
grid: Grid2D,
degree: int,
):
shape = SquareNonConformingPolynomialShapeFunctions(degree)
topology = Grid2DDiscontinuousSpaceTopology(grid, shape=shape)
super().__init__(topology=topology, shape=shape)
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