def test_calculus_2d_4():
DIM = 2
domain = Domain('Omega', dim=DIM)
V = ScalarFunctionSpace('V', domain, kind=None)
u, v = elements_of(V, names='u, v')
a = Constant('a', is_real=True)
# ... jump operator
assert (jump(u + v) == jump(u) + jump(v))
assert (jump(a * u) == a * jump(u))
# ...
# ... avg operator
assert (avg(u + v) == avg(u) + avg(v))
assert (avg(a * u) == a * avg(u))
# ...
# ... Dn operator
assert (Dn(u + v) == Dn(u) + Dn(v))
assert (Dn(a * u) == a * Dn(u))
# ...
# ... minus operator
assert (minus(u + v) == minus(u) + minus(v))
assert (minus(a * u) == a * minus(u))
# ...
# ... plus operator
assert (plus(u + v) == plus(u) + plus(v))
assert (plus(a * u) == a * plus(u))
def test_interface_2d_1():
# ...
def two_patches():
from sympde.topology import InteriorDomain
from sympde.topology import Connectivity, Interface
A = Square('A')
B = Square('B')
A = A.interior
B = B.interior
connectivity = Connectivity()
bnd_A_1 = Boundary(r'\Gamma_1', A, axis=0, ext=-1)
bnd_A_2 = Boundary(r'\Gamma_2', A, axis=0, ext=1)
bnd_A_3 = Boundary(r'\Gamma_3', A, axis=1, ext=-1)
bnd_A_4 = Boundary(r'\Gamma_4', A, axis=1, ext=1)
bnd_B_1 = Boundary(r'\Gamma_1', B, axis=0, ext=-1)
bnd_B_2 = Boundary(r'\Gamma_2', B, axis=0, ext=1)
bnd_B_3 = Boundary(r'\Gamma_3', B, axis=1, ext=-1)
bnd_B_4 = Boundary(r'\Gamma_4', B, axis=1, ext=1)
connectivity['I'] = Interface('I', bnd_A_2, bnd_B_1)
Omega = Domain('Omega',
interiors=[A, B],
boundaries=[
bnd_A_1, bnd_A_2, bnd_A_3, bnd_A_4, bnd_B_1,
bnd_B_2, bnd_B_3, bnd_B_4
],
connectivity=connectivity)
return Omega
# ...
# create a domain with an interface
domain = two_patches()
interfaces = domain.interfaces
V = ScalarFunctionSpace('V', domain)
u, v = elements_of(V, names='u, v')
print(integral(interfaces, u * v))
expr = integral(domain, dot(grad(v), grad(u)))
expr += integral(interfaces, -avg(Dn(u)) * jump(v) + avg(Dn(v)) * jump(u))
a = BilinearForm((u, v), expr)
print(a)