assigning different values to u in subdomains

Question

I have a rectangular domain, divided into two sub domains. I have a time dependent problem to be solved. I would like the second sub domain to act as a sponge layer, damping out the function values in this sub domain. I would like to do this manually by directly assigning in the loop $$u_1 = u$$ in sub domain 0 and $$u_1 = \mu u$$ in sub domain 1 where $$\mu \in (0,1)$$ . Can this be done, and if so, how? I've tried to give the relevant parts of my code below. Any help is greatly appreciated!

# I've defined the function spaces, trial functions,
# test functions and all that here

cf = CellFunction("size_t", mesh, 0)
o2 = AutoSubDomain(lambda x: x[0] > 1)
o2.mark(cf, 1)

# I've defined all initial conditions, functions, boundary
# conditions and the variational forms here

u = Function(V)
t = dt
while t < T+DOLFIN_EPS:
    bc.t = t
    begin("Computing at time t=%g" %g)
    b = assemble(rhs(F))
    bc.apply(A, b)
    solve(A, u.vector(), b)
    end()

    # Here, I want u1 to assign u in sub domain 0, 
    # and I want u to assign mu * u in subdomain 1 
    u1.assign(u)

    t += dt

MiroK · Answer 1 · Mar 4, 2014

Hi, here are two options that I can think of

from dolfin import *

mesh = UnitSquareMesh(100, 100)
V = FunctionSpace(mesh, 'CG', 1)

cf = CellFunction('size_t', mesh, 0)
o1 = AutoSubDomain(lambda x : x[1] >= x[0] - DOLFIN_EPS)
o1.mark(cf, 1)

mu = 100

# using dofmap
dofmap = V.dofmap()
o0_dofs = []
o1_dofs = []

for cell in cells(mesh): # compute dofs in the domains
    if cf[cell] == 0:
        o0_dofs.extend(dofmap.cell_dofs(cell.index()))
    else:
        o1_dofs.extend(dofmap.cell_dofs(cell.index()))

# unique
o0_dofs = list(set(o0_dofs))
o1_dofs = list(set(o1_dofs))

u = interpolate(Expression("x[0]*x[0]"), V)
u1 = Function(V)

u1.vector()[o0_dofs] = u.vector()[o0_dofs]
u1.vector()[o1_dofs] = mu*u.vector()[o1_dofs]

plot(u1)

#using characteristic function
v1 = Function(V)

chi0 = Function(V)
chi1 = Function(V)

for cell in cells(mesh): # set the characteristic functions
    if cf[cell] == 0:
        chi0.vector()[dofmap.cell_dofs(cell.index())] = 1
    else:
        chi1.vector()[dofmap.cell_dofs(cell.index())] = 1

v1 = project(chi0*u, V)
v1 += project(chi1*mu*u, V)

plot(v1)
interactive()

Note that the characteristic functions approach fails in parallel. — pf4d, Jul 23, 2014

assigning different values to u in subdomains

1 Answer