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_interface_integral_1():
# ...
A = Square('A')
B = Square('B')
domain = A.join(B,
name='domain',
bnd_minus=A.get_boundary(axis=0, ext=1),
bnd_plus=B.get_boundary(axis=0, ext=-1))
# ...
x, y = domain.coordinates
V = ScalarFunctionSpace('V', domain, kind=None)
assert (V.is_broken)
u, v = elements_of(V, names='u, v')
# ...
I = domain.interfaces
# ...
# expr = minus(Dn(u))
# print(expr)
# import sys; sys.exit(0)
# ... bilinear forms
# a = BilinearForm((u,v), integral(domain, u*v))
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v))))
# a = BilinearForm((u,v), integral(I, jump(u) * jump(v)))
# a = BilinearForm((u,v), integral(I, jump(Dn(u)) * jump(v)))
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v)))
# + integral(I, jump(u) * jump(v)))
# Nitsch
kappa = Constant('kappa')
expr_I = (-jump(u) * jump(Dn(v)) + kappa * jump(u) * jump(v) +
plus(Dn(u)) * minus(v) + minus(Dn(u)) * plus(v))
a = BilinearForm(
(u, v),
integral(domain, dot(grad(u), grad(v))) + integral(I, expr_I))
# # TODO BUG
# bnd_A = A.get_boundary(axis=0, ext=1)
#
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v)))
# + integral(I, jump(u) * jump(v))
# + integral(bnd_A, dx(u)*v))
expr = TerminalExpr(a)
print(expr)
def test_interface_integral_3():
# ...
A = Square('A')
B = Square('B')
C = Square('C')
AB = A.join(B,
name='AB',
bnd_minus=A.get_boundary(axis=0, ext=1),
bnd_plus=B.get_boundary(axis=0, ext=-1))
domain = AB.join(C,
name='domain',
bnd_minus=B.get_boundary(axis=0, ext=1),
bnd_plus=C.get_boundary(axis=0, ext=-1))
# ...
x, y = domain.coordinates
V = ScalarFunctionSpace('V', domain, kind=None)
assert (V.is_broken)
u, v = elements_of(V, names='u, v')
# ...
I = domain.interfaces
# print(I)
# print(integral(I, jump(u) * jump(v)))
# a = BilinearForm((u,v), integral(domain, u*v))
# a = BilinearForm((u,v), integral(domain, dot(grad(u),grad(v))))
# a = BilinearForm((u,v), integral(I, jump(u) * jump(v)))
a = BilinearForm((u, v),
integral(domain, dot(grad(u), grad(v))) +
integral(I,
jump(u) * jump(v)))
expr = TerminalExpr(a)
print(expr)
# ...
# ... linear forms
b = LinearForm(
v,
integral(domain,
sin(x + y) * v) + integral(I,
cos(x + y) * jump(v)))
expr = TerminalExpr(b)
print(expr)
def test_interface_integral_2():
# ...
A = Square('A')
B = Square('B')
domain = A.join(B,
name='domain',
bnd_minus=A.get_boundary(axis=0, ext=1),
bnd_plus=B.get_boundary(axis=0, ext=-1))
# ...
x, y = domain.coordinates
V = ScalarFunctionSpace('V', domain, kind=None)
assert (V.is_broken)
u, u1, u2, u3 = elements_of(V, names='u, u1, u2, u3')
v, v1, v2, v3 = elements_of(V, names='v, v1, v2, v3')
# ...
I = domain.interfaces
a = BilinearForm((u, v), integral(domain, dot(grad(u), grad(v))))
b = BilinearForm((u, v), integral(I, jump(u) * jump(v)))
A = BilinearForm(((u1, u2), (v1, v2)),
a(u1, v1) + a(u2, v2) + b(u1, v1) + b(u2, v2) + b(u1, v2))
B = BilinearForm(
((u1, u2, u3), (v1, v2, v3)),
a(u1, v1) + a(u2, v2) + a(u3, v3) + b(u1, v1) + b(u2, v2) + b(u1, v2))
print(TerminalExpr(A))
print(TerminalExpr(B))
# ...
# ... linear forms
b = LinearForm(v, integral(I, jump(v)))
b = LinearForm((v1, v2), b(v1) + b(v2))
expr = TerminalExpr(b)
print(expr)
def test_domain_join_square():
# ... line
A = Square('A')
B = Square('B')
C = Square('C')
# ...
# ...
AB = A.join(B, name = 'AB',
bnd_minus = A.get_boundary(axis=0, ext=1),
bnd_plus = B.get_boundary(axis=0, ext=-1))
print(AB)
print(AB.interior)
print(AB.interfaces)
print(AB.connectivity)
print('')
# ...
# ...
AB = A.join(B, name = 'AB',
bnd_minus = A.get_boundary(axis=0, ext=1),
bnd_plus = B.get_boundary(axis=0, ext=-1))
ABC = AB.join(C, name = 'ABC',
bnd_minus = B.get_boundary(axis=0, ext=1),
bnd_plus = C.get_boundary(axis=0, ext=-1))
print(ABC)
print(ABC.interior)
print(ABC.interfaces)
print(list(ABC.connectivity.items()))
print('')
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('')
