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
|
from mpi4py import MPI
import numpy as np
import pytest
import basix.ufl
import dolfinx
import ufl
@pytest.mark.parametrize(
"dtype",
[
np.float32,
np.float64,
pytest.param(np.complex64, marks=pytest.mark.xfail_win32_complex),
pytest.param(np.complex128, marks=pytest.mark.xfail_win32_complex),
],
)
def test_compiled_form(dtype):
"""
Compile a form without an associated mesh and assemble a form over a sequence of meshes
"""
real_type = dtype(0).real.dtype
c_el = basix.ufl.element("Lagrange", "triangle", 1, shape=(2,), dtype=real_type)
domain = ufl.Mesh(c_el)
el = basix.ufl.element("Lagrange", "triangle", 2, dtype=real_type)
V = ufl.FunctionSpace(domain, el)
u = ufl.Coefficient(V)
w = ufl.Coefficient(V)
c = ufl.Constant(domain)
e = ufl.Constant(domain)
J = c * e * u * w * ufl.dx(domain=domain)
# Compile form using dolfinx.jit.ffcx_jit
compiled_form = dolfinx.fem.compile_form(
MPI.COMM_WORLD, J, form_compiler_options={"scalar_type": dtype}
)
def create_and_integrate(N, compiled_form):
mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, N, N, dtype=real_type)
assert mesh.ufl_domain().ufl_coordinate_element() == c_el
Vh = dolfinx.fem.functionspace(mesh, u.ufl_element())
uh = dolfinx.fem.Function(Vh, dtype=dtype)
uh.interpolate(lambda x: x[0])
wh = dolfinx.fem.Function(Vh, dtype=dtype)
wh.interpolate(lambda x: x[1])
eh = dolfinx.fem.Constant(mesh, dtype(3.0))
ch = dolfinx.fem.Constant(mesh, dtype(2.0))
form = dolfinx.fem.create_form(compiled_form, [], mesh, {}, {u: uh, w: wh}, {c: ch, e: eh})
assert np.isclose(mesh.comm.allreduce(dolfinx.fem.assemble_scalar(form), op=MPI.SUM), 1.5)
# Create various meshes, that all uses this compiled form with a map from ufl
# to dolfinx functions and constants
for i in range(1, 4):
create_and_integrate(i, compiled_form)
@pytest.mark.parametrize(
"dtype",
[
np.float32,
np.float64,
pytest.param(np.complex64, marks=pytest.mark.xfail_win32_complex),
pytest.param(np.complex128, marks=pytest.mark.xfail_win32_complex),
],
)
def test_submesh_assembly(dtype):
"""
Compile a form without an associated mesh and assemble a form over a sequence of meshes
"""
real_type = dtype(0).real.dtype
c_el = basix.ufl.element("Lagrange", "triangle", 1, shape=(2,), dtype=real_type)
domain = ufl.Mesh(c_el)
el = basix.ufl.element("Lagrange", "triangle", 2, dtype=real_type)
V = ufl.FunctionSpace(domain, el)
u = ufl.TestFunction(V)
f_el = basix.ufl.element("Lagrange", "interval", 1, shape=(2,), dtype=real_type)
submesh = ufl.Mesh(f_el)
sub_el = basix.ufl.element("Lagrange", "interval", 3, dtype=real_type)
V_sub = ufl.FunctionSpace(submesh, sub_el)
w = ufl.Coefficient(V_sub)
subdomain_id = 3
J = ufl.inner(w, u) * ufl.ds(domain=domain, subdomain_id=subdomain_id)
# Compile form using dolfinx.jit.ffcx_jit
compiled_form = dolfinx.fem.compile_form(
MPI.COMM_WORLD, J, form_compiler_options={"scalar_type": dtype}
)
def create_and_integrate(N, compiled_form):
mesh = dolfinx.mesh.create_rectangle(
MPI.COMM_WORLD,
[np.array([0, 0]), np.array([2, 2])],
[N, N],
dolfinx.mesh.CellType.triangle,
dtype=real_type,
)
assert mesh.ufl_domain().ufl_coordinate_element() == c_el
facets = dolfinx.mesh.locate_entities_boundary(
mesh, mesh.topology.dim - 1, lambda x: np.isclose(x[1], 2)
)
submesh, sub_to_parent, _, _ = dolfinx.mesh.create_submesh(
mesh, mesh.topology.dim - 1, facets
)
imap = mesh.topology.index_map(mesh.topology.dim - 1)
num_facets = imap.size_local + imap.num_ghosts
parent_to_sub = np.full(num_facets, -1, dtype=np.int32)
parent_to_sub[sub_to_parent] = np.arange(sub_to_parent.size, dtype=np.int32)
def g(x):
return -3 * x[1] ** 3 + x[0]
Vh = dolfinx.fem.functionspace(mesh, u.ufl_element())
Wh = dolfinx.fem.functionspace(submesh, w.ufl_element())
wh = dolfinx.fem.Function(Wh, dtype=dtype)
wh.interpolate(g)
facet_entities = dolfinx.fem.compute_integration_domains(
dolfinx.fem.IntegralType.exterior_facet,
mesh.topology,
sub_to_parent,
mesh.topology.dim - 1,
)
subdomains = {dolfinx.fem.IntegralType.exterior_facet: [(subdomain_id, facet_entities)]}
form = dolfinx.fem.create_form(
compiled_form, [Vh], mesh, subdomains, {w: wh}, {}, {submesh: parent_to_sub}
)
# Compute exact solution
x = ufl.SpatialCoordinate(mesh)
ff = dolfinx.mesh.meshtags(
mesh, mesh.topology.dim - 1, facets, np.full(len(facets), subdomain_id, dtype=np.int32)
)
vh = ufl.TestFunction(Vh)
ex_solution = dolfinx.fem.assemble_vector(
dolfinx.fem.form(
ufl.inner(g(x), vh)
* ufl.ds(domain=mesh, subdomain_data=ff, subdomain_id=subdomain_id),
dtype=dtype,
)
)
ex_solution.scatter_reverse(dolfinx.la.InsertMode.add)
bh = dolfinx.fem.assemble_vector(form)
bh.scatter_reverse(dolfinx.la.InsertMode.add)
tol = float(5e2 * np.finfo(dtype).resolution)
np.testing.assert_allclose(ex_solution.array, bh.array, atol=tol)
# Create various meshes, that all uses this compiled form with a map from ufl
# to dolfinx functions and constants
for i in range(1, 4):
create_and_integrate(i, compiled_form)
|
