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import pytest
from utils import LagrangeElement
from ufl import (
Coefficient,
Cofunction,
Form,
FormSum,
FunctionSpace,
Mesh,
SpatialCoordinate,
TestFunction,
TrialFunction,
action,
derivative,
dot,
ds,
dx,
grad,
inner,
nabla_grad,
triangle,
)
from ufl.form import BaseForm
@pytest.fixture
def element():
cell = triangle
element = LagrangeElement(cell, 1)
return element
@pytest.fixture
def domain():
cell = triangle
return Mesh(LagrangeElement(cell, 1, (2,)))
@pytest.fixture
def mass(domain):
cell = triangle
element = LagrangeElement(cell, 1)
space = FunctionSpace(domain, element)
v = TestFunction(space)
u = TrialFunction(space)
return u * v * dx
@pytest.fixture
def stiffness(domain):
cell = triangle
element = LagrangeElement(cell, 1)
space = FunctionSpace(domain, element)
v = TestFunction(space)
u = TrialFunction(space)
return inner(grad(u), grad(v)) * dx
@pytest.fixture
def convection(domain):
cell = triangle
element = LagrangeElement(cell, 1, (2,))
space = FunctionSpace(domain, element)
v = TestFunction(space)
u = TrialFunction(space)
w = Coefficient(space)
return dot(dot(w, nabla_grad(u)), v) * dx
@pytest.fixture
def load(domain):
cell = triangle
element = LagrangeElement(cell, 1)
space = FunctionSpace(domain, element)
f = Coefficient(space)
v = TestFunction(space)
return f * v * dx
@pytest.fixture
def boundary_load(domain):
cell = triangle
element = LagrangeElement(cell, 1)
space = FunctionSpace(domain, element)
f = Coefficient(space)
v = TestFunction(space)
return f * v * ds
def test_form_arguments(mass, stiffness, convection, load):
v, u = mass.arguments()
(f,) = load.coefficients()
assert v.number() == 0
assert u.number() == 1
assert stiffness.arguments() == (v, u)
assert load.arguments() == (v,)
assert (v * dx).arguments() == (v,)
assert (v * dx + v * ds).arguments() == (v,)
assert (v * dx + f * v * ds).arguments() == (v,)
assert (u * v * dx(1) + v * u * dx(2)).arguments() == (v, u)
assert ((f * v) * u * dx + (u * 3) * (v / 2) * dx(2)).arguments() == (v, u)
def test_form_coefficients(element, domain):
space = FunctionSpace(domain, element)
v = TestFunction(space)
f = Coefficient(space)
g = Coefficient(space)
assert (g * dx).coefficients() == (g,)
assert (g * dx + g * ds).coefficients() == (g,)
assert (g * dx + f * ds).coefficients() == (f, g)
assert (g * dx(1) + f * dx(2)).coefficients() == (f, g)
assert (g * v * dx + f * v * dx(2)).coefficients() == (f, g)
def test_form_domains():
cell = triangle
element = LagrangeElement(cell, 1)
domain = Mesh(LagrangeElement(cell, 1, (2,)))
V = FunctionSpace(domain, element)
v = TestFunction(V)
f = Coefficient(V)
x = SpatialCoordinate(domain)[0]
assert (x * dx).ufl_domains() == (domain,)
assert (v * dx).ufl_domains() == (domain,)
assert (f * dx).ufl_domains() == (domain,)
assert (x * v * f * dx).ufl_domains() == (domain,)
assert (1 * dx(domain)).ufl_domains() == (domain,)
def test_form_empty(mass):
assert not mass.empty()
assert Form([]).empty()
def test_form_integrals(mass, boundary_load):
assert isinstance(mass.integrals(), tuple)
assert len(mass.integrals()) == 1
assert mass.integrals()[0].integral_type() == "cell"
assert mass.integrals_by_type("cell") == mass.integrals()
assert mass.integrals_by_type("exterior_facet") == ()
assert isinstance(boundary_load.integrals_by_type("cell"), tuple)
assert len(boundary_load.integrals_by_type("cell")) == 0
assert len(boundary_load.integrals_by_type("exterior_facet")) == 1
def test_form_call():
element = LagrangeElement(triangle, 1)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
V = FunctionSpace(domain, element)
v = TestFunction(V)
u = TrialFunction(V)
f = Coefficient(V)
g = Coefficient(V)
a = g * inner(grad(v), grad(u)) * dx
M = a(f, f, coefficients={g: 1})
assert M == grad(f) ** 2 * dx
import sys
if sys.version_info.major >= 3 and sys.version_info.minor >= 5:
a = u * v * dx
M = eval("(a @ f) @ g")
assert M == g * f * dx
def test_formsum(mass):
element = LagrangeElement(triangle, 1)
domain = Mesh(LagrangeElement(triangle, 1, (2,)))
V = FunctionSpace(domain, element)
v = Cofunction(V.dual())
u = Coefficient(V)
assert v + mass
assert mass + v
assert isinstance((mass + v), FormSum)
assert len((mass + v + v).components()) == 3
# Variational forms are summed appropriately
assert len((mass + v + mass).components()) == 2
assert v - mass
assert mass - v
assert isinstance((mass + v), FormSum)
assert -v
assert isinstance(-v, BaseForm)
assert (-v).weights()[0] == -1
assert 2 * v
assert isinstance(2 * v, BaseForm)
assert (2 * v).weights()[0] == 2
f = action(-v, u)
df = derivative(9 * f, u)
assert isinstance(f, FormSum)
assert f.weights()[0] == -1
assert isinstance(df, FormSum)
assert df.weights()[0] == -9
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