k0 = 20
# approximation space polynomial degree
deg = 1
# number of elements in each direction of mesh
n_elem = 128
mesh = UnitSquareMesh(MPI.comm_world, n_elem, n_elem)
n = FacetNormal(mesh)
# Incident plane wave
theta = np.pi / 8
ui = Expression('exp(j*k0*(cos(theta)*x[0] + sin(theta)*x[1]))',
k0=k0,
theta=theta,
degree=deg + 3,
domain=mesh.ufl_domain())
# Test and trial function space
V = FunctionSpace(mesh, "Lagrange", deg)
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
g = dot(grad(ui), n) + 1j * k0 * ui
a = inner(grad(u), grad(v)) * dx - k0**2 * inner(u, v) * dx + \
1j * k0 * inner(u, v) * ds
L = inner(g, v) * ds
# Compute solution
u = Function(V)
solve(a == L, u, [])
