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
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
|
# Copyright (C) 2009-2020 Garth N. Wells, Matthew W. Scroggs and Jorgen S. Dokken
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Unit tests for dofmap construction"""
import random
from mpi4py import MPI
import numpy as np
import pytest
import ufl
from basix.ufl import element
from dolfinx import default_real_type
from dolfinx.fem import Function, assemble_scalar, form, functionspace
from dolfinx.mesh import create_mesh
def randomly_ordered_mesh(cell_type):
"""Create a randomly ordered mesh to use in the test."""
random.seed(6)
if cell_type == "triangle" or cell_type == "quadrilateral":
gdim = 2
elif cell_type == "tetrahedron" or cell_type == "hexahedron":
gdim = 3
domain = ufl.Mesh(element("Lagrange", cell_type, 1, shape=(gdim,), dtype=default_real_type))
# Create a mesh
if MPI.COMM_WORLD.rank == 0:
N = 6
if cell_type == "triangle" or cell_type == "quadrilateral":
temp_points = np.array([[x / 2, y / 2] for y in range(N) for x in range(N)])
elif cell_type == "tetrahedron" or cell_type == "hexahedron":
temp_points = np.array(
[[x / 2, y / 2, z / 2] for z in range(N) for y in range(N) for x in range(N)]
)
order = [i for i, j in enumerate(temp_points)]
random.shuffle(order)
points = np.zeros(temp_points.shape, dtype=default_real_type)
for i, j in enumerate(order):
points[j] = temp_points[i]
if cell_type == "triangle":
# Make triangle cells using the randomly ordered points
cells = []
for x in range(N - 1):
for y in range(N - 1):
a = N * y + x
# Adds two triangle cells:
# a+N -- a+N+1
# | / |
# | / |
# | / |
# a --- a+1
for cell in [[a, a + 1, a + N + 1], [a, a + N + 1, a + N]]:
cells.append([order[i] for i in cell])
elif cell_type == "quadrilateral":
cells = []
for x in range(N - 1):
for y in range(N - 1):
a = N * y + x
cell = [order[i] for i in [a, a + 1, a + N, a + N + 1]]
cells.append(cell)
elif cell_type == "tetrahedron":
cells = []
for x in range(N - 1):
for y in range(N - 1):
for z in range(N - 1):
a = N**2 * z + N * y + x
for c in [
[a + N, a + N**2 + 1, a, a + 1],
[a + N, a + N**2 + 1, a + 1, a + N + 1],
[a + N, a + N**2 + 1, a + N + 1, a + N**2 + N + 1],
[a + N, a + N**2 + 1, a + N**2 + N + 1, a + N**2 + N],
[a + N, a + N**2 + 1, a + N**2 + N, a + N**2],
[a + N, a + N**2 + 1, a + N**2, a],
]:
cell = [order[i] for i in c]
cells.append(cell)
elif cell_type == "hexahedron":
cells = []
for x in range(N - 1):
for y in range(N - 1):
for z in range(N - 1):
a = N**2 * z + N * y + x
cell = [
order[i]
for i in [
a,
a + 1,
a + N,
a + N + 1,
a + N**2,
a + 1 + N**2,
a + N + N**2,
a + N + 1 + N**2,
]
]
cells.append(cell)
# On process 0, input mesh data and distribute to other
# processes
return create_mesh(MPI.COMM_WORLD, cells, points, domain)
else:
if cell_type == "triangle":
return create_mesh(
MPI.COMM_WORLD,
np.ndarray((0, 3)),
np.ndarray((0, 2), dtype=default_real_type),
domain,
)
elif cell_type == "quadrilateral":
return create_mesh(
MPI.COMM_WORLD,
np.ndarray((0, 4)),
np.ndarray((0, 2), dtype=default_real_type),
domain,
)
elif cell_type == "tetrahedron":
return create_mesh(
MPI.COMM_WORLD,
np.ndarray((0, 4)),
np.ndarray((0, 3), dtype=default_real_type),
domain,
)
elif cell_type == "hexahedron":
return create_mesh(
MPI.COMM_WORLD,
np.ndarray((0, 8)),
np.ndarray((0, 3), dtype=default_real_type),
domain,
)
@pytest.mark.parametrize("space_type", [("P", 1), ("P", 2), ("P", 3), ("P", 4)])
@pytest.mark.parametrize("cell_type", ["triangle", "tetrahedron", "quadrilateral", "hexahedron"])
def test_dof_positions(cell_type, space_type):
"""Checks that dofs on shared triangle edges match up"""
mesh = randomly_ordered_mesh(cell_type)
if cell_type == "triangle":
entities_per_cell = [3, 3, 1]
elif cell_type == "quadrilateral":
entities_per_cell = [4, 4, 1]
elif cell_type == "tetrahedron":
entities_per_cell = [4, 6, 4, 1]
elif cell_type == "hexahedron":
entities_per_cell = [8, 12, 6, 1]
# Get coordinates of dofs and edges and check that they are the same
# for each global dof number
coord_dofs = mesh.geometry.dofmap
x_g = mesh.geometry.x
cmap = mesh.geometry.cmap
tdim = mesh.topology.dim
V = functionspace(mesh, space_type)
entities = {i: {} for i in range(1, tdim)}
for cell in range(coord_dofs.shape[0]):
# Push coordinates forward
X = V.element.interpolation_points()
xg = x_g[coord_dofs[cell], :tdim]
x = cmap.push_forward(X, xg)
dofs = V.dofmap.cell_dofs(cell)
for entity_dim in range(1, tdim):
entity_dofs_local = []
for i in range(entities_per_cell[entity_dim]):
entity_dofs_local += list(V.dofmap.dof_layout.entity_dofs(entity_dim, i))
entity_dofs = [dofs[i] for i in entity_dofs_local]
for i, j in zip(entity_dofs, x[entity_dofs_local]):
if i in entities[entity_dim]:
assert np.allclose(j, entities[entity_dim][i], atol=1e-06)
else:
entities[entity_dim][i] = j
def random_evaluation_mesh(cell_type):
random.seed(6)
if cell_type == "triangle" or cell_type == "quadrilateral":
gdim = 2
elif cell_type == "tetrahedron" or cell_type == "hexahedron":
gdim = 3
domain = ufl.Mesh(element("Lagrange", cell_type, 1, shape=(gdim,), dtype=default_real_type))
if cell_type == "triangle":
temp_points = np.array(
[[-1.0, -1.0], [0.0, 0.0], [1.0, 0.0], [0.0, 1.0]], dtype=default_real_type
)
temp_cells = [[0, 1, 3], [1, 2, 3]]
elif cell_type == "quadrilateral":
temp_points = np.array(
[[-1.0, -1.0], [0.0, 0.0], [1.0, 0.0], [-1.0, 1.0], [0.0, 1.0], [2.0, 2.0]],
dtype=default_real_type,
)
temp_cells = [[0, 1, 3, 4], [1, 2, 4, 5]]
elif cell_type == "tetrahedron":
temp_points = np.array(
[[-1.0, 0.0, -1.0], [0.0, 0.0, 0.0], [1.0, 0.0, 1.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]],
dtype=default_real_type,
)
temp_cells = [[0, 1, 3, 4], [1, 2, 3, 4]]
elif cell_type == "hexahedron":
temp_points = np.array(
[
[-1.0, 0.0, -1.0],
[0.0, 0.0, 0.0],
[1.0, 0.0, 1.0],
[-1.0, 1.0, 1.0],
[0.0, 1.0, 0.0],
[1.0, 1.0, 1.0],
[-1.0, 0.0, 0.0],
[0.0, 0.0, 1.0],
[1.0, 0.0, 2.0],
[-1.0, 1.0, 2.0],
[0.0, 1.0, 1.0],
[1.0, 1.0, 2.0],
],
dtype=default_real_type,
)
temp_cells = [[0, 1, 3, 4, 6, 7, 9, 10], [1, 2, 4, 5, 7, 8, 10, 11]]
order = [i for i, j in enumerate(temp_points)]
random.shuffle(order)
points = np.zeros(temp_points.shape, dtype=default_real_type)
for i, j in enumerate(order):
points[j] = temp_points[i]
cells = []
for cell in temp_cells:
# Randomly number the cell
if cell_type == "triangle":
cell_order = list(range(3))
random.shuffle(cell_order)
elif cell_type == "quadrilateral":
connections = {0: [1, 2], 1: [0, 3], 2: [0, 3], 3: [1, 2]}
start = random.choice(range(4))
cell_order = [start]
for i in range(2):
diff = (
random.choice([i for i in connections[start] if i not in cell_order])
- cell_order[0]
)
cell_order += [c + diff for c in cell_order]
elif cell_type == "tetrahedron":
cell_order = list(range(4))
random.shuffle(cell_order)
elif cell_type == "hexahedron":
connections = {
0: [1, 2, 4],
1: [0, 3, 5],
2: [0, 3, 6],
3: [1, 2, 7],
4: [0, 5, 6],
5: [1, 4, 7],
6: [2, 4, 7],
7: [3, 5, 6],
}
start = random.choice(range(8))
cell_order = [start]
for i in range(3):
diff = (
random.choice([i for i in connections[start] if i not in cell_order])
- cell_order[0]
)
cell_order += [c + diff for c in cell_order]
cells.append([order[cell[i]] for i in cell_order])
return create_mesh(MPI.COMM_WORLD, np.array(cells), points, domain)
@pytest.mark.skip_in_parallel
@pytest.mark.parametrize(
"cell_type,space_type",
[(c, s) for c in ["triangle", "tetrahedron"] for s in ["P", "N1curl", "RT", "BDM", "N2curl"]]
+ [("quadrilateral", s) for s in ["Q", "S", "RTCE", "RTCF", "BDMCE", "BDMCF"]]
+ [("hexahedron", s) for s in ["Q", "S", "NCE", "NCF", "AAE", "AAF"]],
)
@pytest.mark.parametrize("space_order", range(1, 4))
def test_evaluation(cell_type, space_type, space_order):
if cell_type == "hexahedron" and space_order > 3:
pytest.skip("Skipping expensive test on hexahedron")
random.seed(4)
for repeat in range(10):
mesh = random_evaluation_mesh(cell_type)
V = functionspace(mesh, (space_type, space_order))
dofs = [i for i in V.dofmap.cell_dofs(0) if i in V.dofmap.cell_dofs(1)]
N = 5
if cell_type == "tetrahedron":
eval_points = np.array(
[[0.0, i / N, j / N] for i in range(N + 1) for j in range(N + 1 - i)],
dtype=default_real_type,
)
elif cell_type == "hexahedron":
eval_points = np.array(
[[0.0, i / N, j / N] for i in range(N + 1) for j in range(N + 1)],
dtype=default_real_type,
)
else:
eval_points = np.array(
[[0.0, i / N, 0.0] for i in range(N + 1)], dtype=default_real_type
)
for d in dofs:
v = Function(V)
v.x.array[:] = [1 if i == d else 0 for i in range(v.x.index_map.size_local)]
values0 = v.eval(eval_points, [0 for i in eval_points])
values1 = v.eval(eval_points, [1 for i in eval_points])
if len(eval_points) == 1:
values0 = [values0]
values1 = [values1]
if space_type in ["RT", "BDM", "RTCF", "NCF", "BDMCF", "AAF"]:
# Hdiv
for i, j in zip(values0, values1):
assert np.isclose(i[0], j[0], rtol=1.0e-5, atol=1.0e-3)
elif space_type in ["N1curl", "N2curl", "RTCE", "NCE", "BDMCE", "AAE"]:
# Hcurl
for i, j in zip(values0, values1):
assert np.allclose(i[1:], j[1:], rtol=1.0e-4, atol=1.0e-2)
else:
assert np.allclose(values0, values1, rtol=1.0e-6, atol=1.0e-4)
@pytest.mark.skip_in_parallel
@pytest.mark.parametrize(
"cell_type,space_type",
[(c, s) for c in ["triangle", "tetrahedron"] for s in ["P", "N1curl", "RT", "BDM", "N2curl"]]
+ [("quadrilateral", s) for s in ["Q", "S", "RTCE", "RTCF", "BDMCE", "BDMCF"]]
+ [("hexahedron", s) for s in ["Q", "S", "NCE", "NCF", "AAE", "AAF"]],
)
@pytest.mark.parametrize("space_order", range(1, 4))
def test_integral(cell_type, space_type, space_order):
if cell_type == "hexahedron" and space_order >= 3:
pytest.skip("Skipping expensive test on hexahedron")
random.seed(4)
for repeat in range(10):
mesh = random_evaluation_mesh(cell_type)
V = functionspace(mesh, (space_type, space_order))
gdim = mesh.geometry.dim
Vvec = functionspace(mesh, ("P", 1, (gdim,)))
dofs = [i for i in V.dofmap.cell_dofs(0) if i in V.dofmap.cell_dofs(1)]
tdim = mesh.topology.dim
for d in dofs:
v = Function(V)
v.x.array[:] = [1 if i == d else 0 for i, _ in enumerate(v.x.array[:])]
if space_type in ["RT", "BDM", "RTCF", "NCF", "BDMCF", "AAF"]:
# Hdiv
def normal(x):
values = np.zeros((tdim, x.shape[1]))
values[0] = [1 for i in values[0]]
return values
n = Function(Vvec)
n.interpolate(normal)
_form = ufl.inner(ufl.jump(v), n) * ufl.dS
elif space_type in ["N1curl", "N2curl", "RTCE", "NCE", "BDMCE", "AAE"]:
# Hcurl
def tangent(x):
values = np.zeros((tdim, x.shape[1]))
values[1] = [1 for i in values[1]]
return values
t = Function(Vvec)
t.interpolate(tangent)
_form = ufl.inner(ufl.jump(v), t) * ufl.dS
if tdim == 3:
def tangent2(x):
values = np.zeros((3, x.shape[1]))
values[2] = [1 for i in values[2]]
return values
t2 = Function(Vvec)
t2.interpolate(tangent2)
_form += ufl.inner(ufl.jump(v), t2) * ufl.dS
else:
_form = ufl.jump(v) * ufl.dS
value = assemble_scalar(form(_form))
assert np.isclose(value, 0.0, rtol=1.0e-6, atol=1.0e-6)
|
