def test_domain_join_square():
# ... line
A = Square('A')
B = Square('B')
C = Square('C')
# ...
# ...
AB_bnd_minus = A.get_boundary(axis=0, ext=1)
AB_bnd_plus = B.get_boundary(axis=0, ext=-1)
AB = A.join(B, name = 'AB',
bnd_minus = AB_bnd_minus,
bnd_plus = AB_bnd_plus)
print(AB)
assert AB.interior == Union(A.interior, B.interior)
assert AB.interfaces == Interface('A|B', AB_bnd_minus, AB_bnd_plus)
print(AB.connectivity)
# ...
BC_bnd_minus = B.get_boundary(axis=0, ext=1)
BC_bnd_plus = C.get_boundary(axis=0, ext=-1)
ABC = AB.join(C, name = 'ABC',
bnd_minus = BC_bnd_minus,
bnd_plus = BC_bnd_plus)
print(ABC)
assert ABC.interior == Union(A.interior, B.interior, C.interior)
assert ABC.interfaces == Union(Interface('A|B', AB_bnd_minus, AB_bnd_plus),Interface('B|C', BC_bnd_minus, BC_bnd_plus))
print(list(ABC.connectivity.items()))
print('')
def test_boundary_2():
Omega_1 = InteriorDomain('Omega_1', dim=2)
Gamma_1 = Boundary('Gamma_1', Omega_1)
Gamma_2 = Boundary('Gamma_2', Omega_1)
Gamma_3 = Boundary('Gamma_3', Omega_1)
Omega = Domain('Omega',
interiors=[Omega_1],
boundaries=[Gamma_1, Gamma_2, Gamma_3])
assert(Omega.boundary == Union(Gamma_1, Gamma_2, Gamma_3))
assert(Omega.boundary.complement(Gamma_1) == Union(Gamma_2, Gamma_3))
assert(Omega.boundary - Gamma_1 == Union(Gamma_2, Gamma_3))
def test_interior_domain():
D1 = InteriorDomain('D1', dim=2)
D2 = InteriorDomain('D2', dim=2)
assert( D1.todict() == OrderedDict([('name', 'D1')]) )
assert( D2.todict() == OrderedDict([('name', 'D2')]) )
assert( Union(D2, D1) == Union(D1, D2) )
D = Union(D1, D2)
assert(D.dim == 2)
assert(len(D) == 2)
assert( D.todict() == [OrderedDict([('name', 'D1')]),
OrderedDict([('name', 'D2')])] )
def test_interior_domain():
D1 = InteriorDomain('D1', dim=2)
D2 = InteriorDomain('D2', dim=2)
assert( D1.todict() == {'name': 'D1'} )
assert( D2.todict() == {'name': 'D2'} )
assert( Union(D2, D1) == Union(D1, D2) )
D = Union(D1, D2)
assert(D.dim == 2)
assert(len(D) == 2)
assert( D.todict() == [{'name': 'D1'},
{'name': 'D2'}] )
def test_boundary_2d_2():
Omega_1 = InteriorDomain('Omega_1', dim=2)
B1 = Boundary('B1', Omega_1)
B2 = Boundary('B2', Omega_1)
B3 = Boundary('B3', Omega_1)
domain = Domain('Omega', interiors=[Omega_1], boundaries=[B1, B2, B3])
V = FunctionSpace('V', domain)
v = TestFunction(V, name='v')
u = TestFunction(V, name='u')
x, y = V.coordinates
alpha = Constant('alpha')
# ...
print('==== l0 ====')
l0 = LinearForm(v, x * y * v, name='l0')
print(evaluate(l0, verbose=VERBOSE))
print('')
# ...
# ...
print('==== l1 ====')
g = Tuple(x**2, y**2)
l1 = LinearForm(v, v * trace_1(g, domain.boundary))
print(evaluate(l1, verbose=VERBOSE))
print('')
# ...
# ...
print('==== l2 ====')
B_neumann = Union(B1, B2)
g = Tuple(x**2, y**2)
l2 = LinearForm(v, v * trace_1(g, B_neumann), name='l2')
print(evaluate(l2, verbose=VERBOSE))
print('')
# ...
# ...
print('==== l3 ====')
l3 = LinearForm(v, l2(v))
assert (l3(v).__str__ == l2(v).__str__)
print(evaluate(l3, verbose=VERBOSE))
print('')
# ...
# ...
print('==== l4 ====')
l4 = LinearForm(v, l0(v) + l2(v))
print(evaluate(l4, verbose=VERBOSE))
print('')
def _get_domain(expr):
# expr is an integral of BasicExpr or Add of Integral of BasicExpr
if isinstance(expr, Integral):
return expr.domain
elif isinstance(expr, (Add, Mul)):
domains = []
for a in expr.args:
a = _get_domain(a)
if isinstance(a, Union):
domains.extend(list(a.args))
elif isinstance(a, BasicDomain):
domains.append(a)
return Union(*domains)
def test_element():
D1 = InteriorDomain('D1', dim=2)
D2 = InteriorDomain('D2', dim=2)
D = Union(D1, D2)
e1 = ElementDomain()
a = Area(e1)
print(a)
a = Area(D1)
print(a)
assert(Area(D) == Area(D1) + Area(D2))
def _get_domain(expr):
# expr is an integral of BasicExpr or Add of Integral of BasicExpr
if isinstance(expr, (DomainIntegral, BoundaryIntegral, InterfaceIntegral)):
return expr.domain
elif isinstance(expr, (Add,Mul)):
domains = set()
for a in expr.args:
a = _get_domain(a)
if isinstance(a, Union):
domains = domains.union(a.args)
elif isinstance(a, BasicDomain):
domains = domains.union([a])
if len(domains) == 1:
return list(domains)[0]
return Union(*domains)
def test_terminal_expr_linear_2d_5(boundary=[r'\Gamma_1', r'\Gamma_3']):
# ... abstract model
domain = Square()
V = ScalarFunctionSpace('V', domain)
B_neumann = [domain.get_boundary(i) for i in boundary]
if len(B_neumann) == 1:
B_neumann = B_neumann[0]
else:
B_neumann = Union(*B_neumann)
x, y = domain.coordinates
nn = NormalVector('nn')
F = element_of(V, name='F')
v = element_of(V, name='v')
u = element_of(V, name='u')
int_0 = lambda expr: integral(domain, expr)
int_1 = lambda expr: integral(B_neumann, expr)
expr = dot(grad(v), grad(u))
a = BilinearForm((v, u), int_0(expr))
solution = cos(0.5 * pi * x) * cos(0.5 * pi * y)
f = (1. / 2.) * pi**2 * solution
expr = f * v
l0 = LinearForm(v, int_0(expr))
expr = v * dot(grad(solution), nn)
l_B_neumann = LinearForm(v, int_1(expr))
expr = l0(v) + l_B_neumann(v)
l = LinearForm(v, expr)
print(TerminalExpr(l))
print('')
def test_terminal_expr_linear_2d_4():
D1 = InteriorDomain('D1', dim=2)
D2 = InteriorDomain('D2', dim=2)
domain = Union(D1, D2)
x, y = domain.coordinates
kappa = Constant('kappa', is_real=True)
mu = Constant('mu', is_real=True)
V = ScalarFunctionSpace('V', domain)
u, u1, u2 = [element_of(V, name=i) for i in ['u', 'u1', 'u2']]
v, v1, v2 = [element_of(V, name=i) for i in ['v', 'v1', 'v2']]
# ...
int_0 = lambda expr: integral(domain, expr)
l = LinearForm(v, int_0(x * y * v))
print(TerminalExpr(l))
print('')