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# Copyright (c) 2024 Matthew Scroggs
# FEniCS Project
# SPDX-License-Identifier: MIT
import numpy as np
import pytest
import basix
from basix import ElementFamily
elements = [
(ElementFamily.P, [basix.LagrangeVariant.equispaced]),
(ElementFamily.P, [basix.LagrangeVariant.gll_warped]),
(ElementFamily.RT, []),
(ElementFamily.BDM, []),
(ElementFamily.N1E, []),
(ElementFamily.N2E, []),
(ElementFamily.Regge, []),
(ElementFamily.HHJ, []),
(ElementFamily.bubble, []),
(ElementFamily.serendipity, [basix.LagrangeVariant.legendre, basix.DPCVariant.legendre]),
(ElementFamily.DPC, [basix.LagrangeVariant.unset, basix.DPCVariant.legendre]),
]
def cross2d(x):
return [x[1], -x[0]]
def create_continuity_map_interval(map_type, start, end):
if map_type == basix.MapType.identity:
return lambda x: x
if map_type == basix.MapType.covariantPiola:
return lambda x: np.dot(x, end - start)
if map_type == basix.MapType.contravariantPiola:
return lambda x: np.dot(x, cross2d(end - start))
if map_type == basix.MapType.doubleCovariantPiola:
return lambda x: np.dot(start - end, np.dot(x, end - start))
if map_type == basix.MapType.doubleContravariantPiola:
return lambda x: np.dot(cross2d(end - start), np.dot(x, cross2d(end - start)))
raise NotImplementedError
def create_continuity_map_triangle(map_type, v0, v1, v2):
if map_type == basix.MapType.identity:
return lambda x: x
raise NotImplementedError
def create_continuity_map_quadrilateral(map_type, v0, v1, v2):
if map_type == basix.MapType.identity:
return lambda x: x
raise NotImplementedError
@pytest.mark.parametrize("degree", range(1, 5))
@pytest.mark.parametrize("element, variant", elements)
def test_continuity_interval_facet(degree, element, variant):
"""Test that continuity between neighbouring cells of different types."""
elements = {}
for cell in [basix.CellType.triangle, basix.CellType.quadrilateral]:
try:
elements[cell] = basix.create_element(element, cell, degree, *variant)
except RuntimeError:
pass
if len(elements) <= 1:
pytest.skip()
facets = [
[
np.array([0, 0]),
np.array([1, 0]),
{basix.CellType.triangle: 2, basix.CellType.quadrilateral: 0},
],
[
np.array([0, 0]),
np.array([0, 1]),
{basix.CellType.triangle: 1, basix.CellType.quadrilateral: 1},
],
]
for start, end, cellmap in facets:
points = np.array([start + i / 10 * (end - start) for i in range(11)])
data = None
for c, e in elements.items():
tab = e.tabulate(0, points)[0]
continuity_map = create_continuity_map_interval(e.map_type, start, end)
entity_tab = [continuity_map(tab[:, i, :]) for i in e.entity_dofs[1][cellmap[c]]]
if data is None:
data = entity_tab
else:
assert np.allclose(data, entity_tab)
@pytest.mark.parametrize("degree", range(1, 5))
@pytest.mark.parametrize("element, variant", elements)
def test_continuity_triangle_facet(degree, element, variant):
"""Test continuity between neighbouring cells of different types."""
elements = {}
# , basix.CellType.pyramid]:
for cell in [basix.CellType.tetrahedron, basix.CellType.prism]:
try:
elements[cell] = basix.create_element(element, cell, degree, *variant)
except RuntimeError:
pass
if len(elements) <= 1:
pytest.skip()
facets = [
[
np.array([0, 0, 0]),
np.array([1, 0, 0]),
np.array([0, 1, 0]),
{basix.CellType.tetrahedron: 3, basix.CellType.prism: 0},
],
[
np.array([0, 0, 0]),
np.array([1, 0, 0]),
np.array([0, 0, 1]),
{basix.CellType.tetrahedron: 2, basix.CellType.pyramid: 1},
],
[
np.array([0, 0, 0]),
np.array([0, 1, 0]),
np.array([0, 0, 1]),
{basix.CellType.tetrahedron: 1, basix.CellType.pyramid: 2},
],
]
for v0, v1, v2, cellmap in facets:
points = np.array(
[v0 + i / 10 * (v1 - v0) + j / 10 * (v2 - v0) for i in range(11) for j in range(11 - i)]
)
data = None
for c, e in elements.items():
if c in cellmap:
tab = e.tabulate(0, points)
continuity_map = create_continuity_map_triangle(e.map_type, v0, v1, v2)
entity_tab = [continuity_map(tab[:, :, i, :]) for i in e.entity_dofs[2][cellmap[c]]]
if data is None:
data = entity_tab
else:
assert np.allclose(data, entity_tab)
@pytest.mark.parametrize("degree", range(1, 5))
@pytest.mark.parametrize("element, variant", elements)
def test_continuity_quadrilateral_facet(degree, element, variant):
"""Test continuity between neighbouring cells of different types."""
elements = {}
# , basix.CellType.pyramid]:
for cell in [basix.CellType.hexahedron, basix.CellType.prism]:
try:
elements[cell] = basix.create_element(element, cell, degree, *variant)
except RuntimeError:
pass
if len(elements) <= 1:
pytest.skip()
facets = [
[
np.array([0, 0, 0]),
np.array([1, 0, 0]),
np.array([0, 1, 0]),
np.array([1, 1, 0]),
{basix.CellType.hexahedron: 0, basix.CellType.pyramid: 0},
],
[
np.array([0, 0, 0]),
np.array([1, 0, 0]),
np.array([0, 0, 1]),
np.array([1, 0, 1]),
{basix.CellType.hexahedron: 1, basix.CellType.prism: 1},
],
[
np.array([0, 0, 0]),
np.array([0, 1, 0]),
np.array([0, 0, 1]),
np.array([0, 1, 1]),
{basix.CellType.hexahedron: 2, basix.CellType.prism: 2},
],
]
for v0, v1, v2, v3, cellmap in facets:
assert np.allclose(v0 + v3, v1 + v2)
points = np.array(
[v0 + i / 10 * (v1 - v0) + j / 10 * (v2 - v0) for i in range(11) for j in range(11)]
)
data = None
for c, e in elements.items():
if c in cellmap:
tab = e.tabulate(0, points)
continuity_map = create_continuity_map_quadrilateral(e.map_type, v0, v1, v2)
entity_tab = [continuity_map(tab[:, :, i, :]) for i in e.entity_dofs[2][cellmap[c]]]
if data is None:
data = entity_tab
else:
assert np.allclose(data, entity_tab)
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