boundary_marker = False
dt = Constant(0)
dt.assign(np.min([fenics_dt, precice_dt]))
# Define variational problem
u = TrialFunction(V)
v = TestFunction(V)
f = Expression('beta + gamma*x[0]*x[0] - 2*gamma*t - 2*(1-gamma) - 2*alpha', degree=2, alpha=alpha,
beta=beta, gamma=gamma, t=0)
F = u * v / dt * dx + dot(grad(u), grad(v)) * dx - (u_n / dt + f) * v * dx
bcs = [DirichletBC(V, u_D, remaining_boundary)]
# Set boundary conditions at coupling interface once wrt to the coupling expression
coupling_expression = precice.create_coupling_expression()
if problem is ProblemType.DIRICHLET:
# modify Dirichlet boundary condition on coupling interface
bcs.append(DirichletBC(V, coupling_expression, coupling_boundary))
if problem is ProblemType.NEUMANN:
# modify Neumann boundary condition on coupling interface, modify weak form correspondingly
if not boundary_marker: # there is only 1 Neumann-BC which is at the coupling boundary -> integration over whole boundary
if coupling_expression.is_scalar_valued():
F += v * coupling_expression * dolfin.ds # this term has to be added to weak form to add a Neumann BC (see e.g. p. 83ff Langtangen, Hans Petter, and Anders Logg. "Solving PDEs in Python The FEniCS Tutorial Volume I." (2016).)
elif coupling_expression.is_vector_valued():
normal = FacetNormal(mesh)
F += -v * dot(normal, coupling_expression) * dolfin.ds
else:
raise Exception("invalid!")
else: # For multiple Neumann BCs integration should only be performed over the respective domain.
# TODO: fix the problem here
u = TrialFunction(V)
v = TestFunction(V)
u_n = Function(V)
if args.source:
u_ini = Expression("1", degree=1)
bc = DirichletBC(V, u_ini, AllBoundary())
elif args.drain:
u_ini = Expression("0", degree=1)
bc = DirichletBC(V, u_ini, RightBoundary())
u_n = interpolate(u_ini, V)
dt = precice.initialize(AllDomain(), read_function_space=V, write_object=u_n)
volume_term = precice.create_coupling_expression()
f = Function(V)
dt_inv = Constant(1 / dt)
diffusion_source = 1
diffusion_drain = 1
if args.source:
F = dt_inv * (u - u_n) * v * dx - (f - u_ini) * v * dx + diffusion_source * inner(grad(u), grad(v)) * dx
elif args.drain:
F = dt_inv * (u - u_n) * v * dx - (f - u) * v * dx + diffusion_drain * inner(grad(u), grad(v)) * dx
# Time-stepping
u_np1 = Function(V)
if args.source: