def test_compiler_3d_2():
domain = Domain('Omega', dim=3)
H1 = ScalarFunctionSpace('V0', domain, kind='H1')
Hcurl = VectorFunctionSpace('V1', domain, kind='Hcurl')
Hdiv = VectorFunctionSpace('V2', domain, kind='Hdiv')
L2 = ScalarFunctionSpace('V3', domain, kind='L2')
V = VectorFunctionSpace('V', domain)
X = H1 * Hcurl * Hdiv * L2
v = element_of(X, name='v0, v1, v2, v3')
u = element_of(X, name='u0, u1, u2, u3')
beta = Field(V, 'beta')
# # ... Dot operator
# expr = dot(u1, v1)
# print(ExteriorCalculusExpr(expr, tests=[v1]))
#
# expr = dot(u2, v2)
# print(ExteriorCalculusExpr(expr, tests=[v2]))
#
# expr = dot(grad(v0), u1)
# print(ExteriorCalculusExpr(expr, tests=[v0]))
#
# expr = dot(grad(u0), v1)
# print(ExteriorCalculusExpr(expr, tests=[v1]))
#
# expr = dot(curl(u1), v2)
# print(ExteriorCalculusExpr(expr, tests=[v2]))
#
# expr = dot(curl(v1), u2)
# print(ExteriorCalculusExpr(expr, tests=[v1]))
# # ...
# ... Mul operator
expr = u[0] * v[0]
print(ExteriorCalculusExpr(expr, tests=[v[0]]))
expr = u[0] * div(v[2])
print(ExteriorCalculusExpr(expr, tests=[v[2]]))
expr = v[0] * div(u[2])
print(ExteriorCalculusExpr(expr, tests=[v[0]]))
def test_compiler_3d_stokes():
domain = Domain('Omega', dim=3)
# ...
# by setting the space type, we cannot evaluate grad of Hdiv function, then
# ArgumentTypeError will be raised.
# In order to avoid this problem, we need first to declare our space as an
# undefined type.
Hdiv = VectorFunctionSpace('V2', domain, kind='Hdiv')
L2 = ScalarFunctionSpace('V3', domain, kind='L2')
X = Hdiv * L2
u, p = element_of(X, name='u, p')
v, q = element_of(X, name='v, q')
with pytest.raises(ArgumentTypeError):
expr = inner(grad(u), grad(v)) - div(v) * p + q * div(u)
# ...
# ...
Hdiv = VectorFunctionSpace('V2', domain)
L2 = ScalarFunctionSpace('V3', domain)
X = Hdiv * L2
u, p = element_of(X, name='u, p')
v, q = element_of(X, name='v, q')
expr = inner(grad(u), grad(v)) - div(v) * p + q * div(u)
atoms = {
u: DifferentialForm('u', index=2, dim=domain.dim),
v: DifferentialForm('v', index=2, dim=domain.dim),
p: DifferentialForm('p', index=3, dim=domain.dim),
q: DifferentialForm('q', index=3, dim=domain.dim)
}
newexpr = ExteriorCalculusExpr(expr, tests=[v, q], atoms=atoms)
print('===== BEFORE =====')
print(newexpr)
newexpr = augmented_expression(newexpr,
tests=[v, q],
atoms=atoms,
weak=False)
print('===== AFTER =====')
print(newexpr)
def test_compiler_3d_poisson():
domain = Domain('Omega', dim=3)
H1 = ScalarFunctionSpace('V0', domain, kind='H1')
Hcurl = VectorFunctionSpace('V1', domain, kind='Hcurl')
Hdiv = VectorFunctionSpace('V2', domain, kind='Hdiv')
L2 = ScalarFunctionSpace('V3', domain, kind='L2')
V = VectorFunctionSpace('V', domain)
X = Hdiv * L2
sigma, u = element_of(X, name='sigma, u')
tau, v = element_of(X, name='tau, v')
expr = dot(sigma, tau) + div(tau) * u + div(sigma) * v
print(ExteriorCalculusExpr(expr, tests=[tau, v]))
def test_compiler_3d_1():
domain = Domain('Omega', dim=3)
H1 = ScalarFunctionSpace('V0', domain, kind='H1')
Hcurl = VectorFunctionSpace('V1', domain, kind='Hcurl')
Hdiv = VectorFunctionSpace('V2', domain, kind='Hdiv')
L2 = ScalarFunctionSpace('V3', domain, kind='L2')
V = VectorFunctionSpace('V', domain)
X = H1 * Hcurl * Hdiv * L2
v0, v1, v2, v3 = element_of(X, name='v0, v1, v2, v3')
beta = element_of(V, 'beta')
# # ...
# expr = grad(v0)
# expected = d(DifferentialForm('v0', index=0, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr) == expected)
# # ...
#
# # ...
# expr = curl(v1)
# expected = d(DifferentialForm('v1', index=1, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr) == expected)
# # ...
#
# # ...
# expr = div(v2)
# expected = d(DifferentialForm('v2', index=2, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr) == expected)
# # ...
#
# # ...
# expr = grad(v0)
# expected = - delta(DifferentialForm('v0', index=3, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr, tests=[v0]) == expected)
# # ...
#
# # ...
# expr = curl(v1)
# expected = delta(DifferentialForm('v1', index=2, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr, tests=[v1]) == expected)
# # ...
#
# # ...
# expr = div(v2)
# expected = -delta(DifferentialForm('v2', index=1, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr, tests=[v2]) == expected)
# # ...
#
# # ...
# expr = dot(beta, v1)
# expected = ip(beta, DifferentialForm('v1', index=1, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr) == expected)
# # ...
#
# # ...
# expr = cross(beta, v2)
# expected = ip(beta, DifferentialForm('v2', index=2, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr) == expected)
# # ...
#
# # ...
# expr = beta*v3
# expected = ip(beta, DifferentialForm('v3', index=3, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr) == expected)
# # ...
#
# # ...
# expr = dot(beta, v1)
# expected = jp(beta, DifferentialForm('v1', index=3, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr, tests=[v1]) == expected)
# # ...
#
# # ...
# expr = cross(beta, v2)
# expected = -jp(beta, DifferentialForm('v2', index=2, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr, tests=[v2]) == expected)
# # ...
#
# # ...
# expr = beta*v3
# expected = jp(beta, DifferentialForm('v3', index=1, dim=domain.dim))
#
# assert(ExteriorCalculusExpr(expr, tests=[v3]) == expected)
# # ...
# ..................................................
# LIE DERIVATIVES
# ..................................................
# ...
expr = dot(beta, grad(v0))
expected = ld(beta, DifferentialForm('v0', index=0, dim=domain.dim))
assert (ExteriorCalculusExpr(expr) == expected)
# ...
# ...
expr = grad(dot(beta, v1)) + cross(curl(v1), beta)
expected = ld(beta, DifferentialForm('v1', index=1, dim=domain.dim))
assert (ExteriorCalculusExpr(expr) == expected)
# ...
# ...
expr = curl(cross(v2, beta)) + div(v2) * beta
expected = ld(beta, DifferentialForm('v2', index=2, dim=domain.dim))
#assert(ExteriorCalculusExpr(expr) == expected)
# ...
# ...
expr = div(beta * v3)
expected = ld(beta, DifferentialForm('v3', index=3, dim=domain.dim))
assert (ExteriorCalculusExpr(expr) == expected)