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"""Unit tests for coordinate derivative"""
# Copyright (C) 2018 Florian Wechsung
#
# This file is part of DOLFIN.
#
# DOLFIN is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# DOLFIN is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
#
# Modified by Florian Wechsung 2018 and Jørgen S. Dokken 2020
import pytest
import numpy as np
from dolfin import *
from ufl_legacy import replace
from ufl_legacy.log import UFLException
from dolfin_utils.test import skip_in_parallel
def test_first_shape_derivative():
mesh = UnitSquareMesh(6, 6)
n = FacetNormal(mesh)
X = SpatialCoordinate(mesh)
x, y = X
V = FunctionSpace(mesh, "Lagrange", 1)
u = project(x*x+y*x+y*y+sin(x)+cos(x), V)
dX = TestFunction(VectorFunctionSpace(mesh, "Lagrange", 1))
def test_first(J, dJ):
computed = assemble(derivative(J, X)).get_local()
actual = assemble(dJ).get_local()
assert np.allclose(computed, actual, rtol=1e-14)
Ja = u * u * dx
dJa = u * u * div(dX) * dx
test_first(Ja, dJa)
Jb = inner(grad(u), grad(u)) * dx
dJb = -2*inner(dot(grad(dX), grad(u)), grad(u)) * dx + inner(grad(u), grad(u)) * div(dX) * dx
test_first(Jb, dJb)
f = x * y * sin(x) * cos(y)
Jc = f * dx
dJc = div(f * dX) * dx
test_first(Jc, dJc)
Jd = f * ds
dJd = inner(grad(f), dX) * ds \
+ f * (div(dX) - inner(dot(grad(dX), n), n)) * ds
test_first(Jd, dJd)
J = Ja + Jb + Jc + Jd
dJ = dJa + dJb + dJc + dJd
test_first(J, dJ)
def test_mixed_derivatives():
mesh = UnitSquareMesh(6, 6)
X = SpatialCoordinate(mesh)
x, y = X
V = FunctionSpace(mesh, "CG", 1)
u = project(x * x + y * x + y * y + sin(x) + cos(x), V)
v = TrialFunction(V)
dX = TestFunction(VectorFunctionSpace(mesh, "Lagrange", 1))
dX_ = TrialFunction(VectorFunctionSpace(mesh, "Lagrange", 1))
def test_mixed(J, dJ_manual):
computed1 = assemble(derivative(derivative(J, X, dX), u)).norm("frobenius")
computed2 = assemble(derivative(derivative(J, u), X, dX_)).norm("frobenius")
computed3 = assemble(derivative(derivative(J, X), u)).norm("frobenius")
computed4 = assemble(derivative(derivative(J, u), X)).norm("frobenius")
actuala = assemble(dJ_manual).norm("frobenius")
assert np.isclose(computed1, actuala, rtol=1e-14)
assert np.isclose(computed2, actuala, rtol=1e-14)
assert np.isclose(computed3, actuala, rtol=1e-14)
assert np.isclose(computed4, actuala, rtol=1e-14)
Ja = u * u * dx
dJa = 2 * u * v * div(dX) * dx
test_mixed(Ja, dJa)
Jb = inner(grad(u), grad(u)) * dx
dJb = 2*inner(grad(u), grad(v)) * div(dX) * dx \
- 2*inner(dot(nabla_grad(dX), grad(u)), grad(v)) * dx \
- 2*inner(grad(u), dot(nabla_grad(dX), grad(v))) * dx
test_mixed(Jb, dJb)
J = Ja + Jb
dJ = dJa + dJb
test_mixed(J, dJ)
def test_second_shape_derivative():
mesh = UnitSquareMesh(6, 6)
V = FunctionSpace(mesh, "CG", 1)
X = SpatialCoordinate(mesh)
x, y = X
u = project(x * x + y * x + y * y + sin(x) + cos(x), V)
Z = VectorFunctionSpace(mesh, "Lagrange", 1)
dX1 = TestFunction(Z)
dX2 = TrialFunction(Z)
def test_second(J, ddJ):
computed = assemble(derivative(derivative(J, X, dX1), X, dX2)).norm("frobenius")
actual = assemble(ddJ).norm("frobenius")
assert np.isclose(computed, actual, rtol=1e-14)
Ja = u * u * dx
ddJa = u * u * div(dX1) * div(dX2) * dx - u * u * tr(grad(dX1)*grad(dX2)) * dx
test_second(Ja, ddJa)
Jb = inner(grad(u), grad(u)) * dx
ddJb = 2*inner(dot(dot(nabla_grad(dX2), nabla_grad(dX1)), grad(u)), grad(u)) * dx \
+ 2*inner(dot(nabla_grad(dX1), dot(nabla_grad(dX2), grad(u))), grad(u)) * dx \
+ 2*inner(dot(nabla_grad(dX1), grad(u)), dot(nabla_grad(dX2), grad(u))) * dx \
- 2*inner(dot(nabla_grad(dX2), grad(u)), grad(u)) * div(dX1) * dx \
- inner(grad(u), grad(u)) * tr(nabla_grad(dX1)*nabla_grad(dX2)) * dx \
- 2*inner(dot(nabla_grad(dX1), grad(u)), grad(u)) * div(dX2) * dx \
+ inner(grad(u), grad(u)) * div(dX1) * div(dX2) * dx
test_second(Jb, ddJb)
test_second(Ja+Jb, ddJa + ddJb)
# In parallel a RuntimeError is thrown instead of the specific
# UFLException, so we skip that case.
@skip_in_parallel
def test_integral_scaling_edge_case():
mesh = UnitSquareMesh(6, 6)
X = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 1)
u = Function(V)
J = u * u * dx
with pytest.raises(UFLException):
assemble(Constant(2.0) * derivative(J, X))
with pytest.raises(UFLException):
assemble(derivative(Constant(2.0) * derivative(J, X), X))
with pytest.raises(UFLException):
assemble(Constant(2.0) * derivative(derivative(J, X), X))
def test_different_quadratures():
"""
Checking that expressions with different quadrature rules
can be assembled as a sum, using the higher order quadrature for all
terms
"""
mesh = UnitIntervalMesh(10)
x = SpatialCoordinate(mesh)
f = x[0]**2
V = FunctionSpace(mesh, "CG", 1)
u, v = TrialFunction(V), TestFunction(V)
a = inner(grad(u), grad(v)) * dx + inner(u, v) * dx
l = f * v * dx
bc = DirichletBC(V, Constant(1), "on_boundary")
uh = Function(V)
solve(a==l, uh, bcs=bc)
F = a - l
J = uh**2 * dx
# Adjoint equation disregarding Dirichlet BC adjoint
dJdu = derivative(J, uh)
dFdu = derivative(action(F, uh), uh)
bc_hom = DirichletBC(V, Constant(0), "on_boundary")
lmbd = Function(V)
solve(dFdu==-dJdu, lmbd, bc_hom)
F = replace(F, {u: uh})
dJdu = replace(dJdu, {u: uh})
# Parts of second order adjoint equation:
S = VectorFunctionSpace(mesh, "CG", 1)
s = Function(S)
F = replace(F, {v: lmbd})
ds = TestFunction(S)
dFdm = derivative(F, x, ds)
d2Fdm2 = derivative(dFdm, x, s)
soas_separated = assemble(d2Fdm2) + assemble(dFdm)
soa = d2Fdm2 + dFdm
soas = assemble(soa)
assert np.isclose(soas_separated.norm("l2"), soas.norm("l2"))
# 2D test for triangles with quadrature degree 3 and 4
mesh = UnitSquareMesh(5, 5)
x = SpatialCoordinate(mesh)
V = FunctionSpace(mesh, "CG", 1)
u0 = cos(pi*x[0])*sin(pi*x[1])
u, v = TrialFunction(V), TestFunction(V)
F = inner(u - u0, v)*dx
uh = Function(V)
solve(lhs(F) == rhs(F), uh)
J = uh**2*dx
# adjoint eq disregarding Dirichlet BC
dJdu = derivative(J, uh)
dFdu = derivative(action(F, uh), uh)
bc_hom = DirichletBC(V, Constant(0), "on_boundary")
lmbd = Function(V)
solve(dFdu==-dJdu, lmbd, bc_hom)
F = replace(F, {u:uh})
dJdu = replace(dJdu, {u: uh})
# Parts of second order adjoint eq:
S = VectorFunctionSpace(mesh, "CG", 1)
s = Function(S)
F = replace(F, {v: lmbd})
ds = TestFunction(S)
dFdm = derivative(F, x, ds)
d2Fdm2 = derivative(dFdm, x, s)
d2Fdudm = derivative(dFdm, uh, lmbd)
soas_separated = assemble(d2Fdm2) + assemble(dFdm) + assemble(d2Fdudm)
soa = d2Fdm2 + d2Fdudm + dFdm
soas = assemble(soa)
assert np.isclose(soas_separated.norm("l2"), soas.norm("l2"))
def test_unique_tables():
"""
Checking that the unique table names in FFC are cached correctly
"""
mesh = UnitIntervalMesh(10)
x = SpatialCoordinate(mesh)
f = x[0]**2
V = FunctionSpace(mesh, "CG", 1)
f = project(f, V)
u, v = TrialFunction(V), TestFunction(V)
a = inner(grad(u), grad(v)) * dx + inner(u, v) * dx
l = f * v * dx
bc = DirichletBC(V, Constant(1), "on_boundary")
uh = Function(V)
solve(a == l, uh, bcs=bc)
F = a - l
J = uh**2 * dx
# Adjoint eq disregarding Dirichlet BC
dJdu = derivative(J, uh)
dFdu = derivative(action(F, uh), uh)
bc_hom = DirichletBC(V, Constant(0), "on_boundary")
lmbd = Function(V)
solve(dFdu == -dJdu, lmbd, bc_hom)
F = replace(F, {u: uh})
dJdu = replace(dJdu, {u: uh})
# Parts of second order adjoint eq:
S = VectorFunctionSpace(mesh, "CG", 1)
s = Function(S)
F = replace(F, {v: lmbd})
ds = TestFunction(S)
dFdm = derivative(F, x, ds)
d2Fdm2 = derivative(dFdm, x, s)
soas_separated = assemble(d2Fdm2) + assemble(dFdm)
soa = d2Fdm2 + dFdm
soas = assemble(soa)
assert np.isclose(soas_separated.norm("l2"), soas.norm("l2"))
if __name__ == "__main__":
import os
pytest.main(os.path.abspath(__file__))
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