Diffusion equation in 3d for multiple subdomains and multiple boundary conditions?

General
1

from dolfin import *

Create classes for defining parts of the boundaries and the interior

of the domain

class Left(SubDomain):
def inside(self, x, on_boundary):
tol= 1E-15
return near(x[0], 0.0,tol)

class Right(SubDomain):
def inside(self, x, on_boundary):
tol= 1E-15
return near(x[0], 1.0,tol)

class Bottom(SubDomain):
def inside(self, x, on_boundary):
tol= 1E-15
return near(x[2], 0.0,tol)

class Top(SubDomain):
def inside(self, x, on_boundary):
tol= 1E-15
return near(x[2], 1.0,tol)

class Outside(SubDomain):
def inside(self, x, on_boundary):
tol= 1E-15
return near(x[1],1.0,tol)
class Inside(SubDomain):
def inside(self, x, on_boundary):
tol= 1E-15
return near(x[1],1.0,tol)

Initialize sub-domain instances

left = Left()
top = Top()
right = Right()
bottom = Bottom()
outside = Outside()
inside = Inside()

Define mesh

mesh = UnitCubeMesh(20,20,20)

Initialize mesh function for interior domains

domains = MeshFunction(‘size_t’,mesh,mesh.topology().dim())
domains.set_all(0)

Initialize mesh function for boundary domains

boundaries = MeshFunction(‘size_t’,mesh,mesh.topology().dim()-1)

boundaries.set_all(0)
left.mark(boundaries, 1)
top.mark(boundaries, 2)
right.mark(boundaries, 3)
bottom.mark(boundaries, 4)
outside.mark(boundaries,5)
inside.mark(boundaries,6)

Define input data

dt=0.1
u_0= Constant(0.0)

g_L = Expression(“- 10*exp(- pow(x[1] - 0.5, 2))”,degree=2)
g_R = Constant(“1.0”)
f = Constant(0.0)

Define function space and basis functions

V = FunctionSpace(mesh, “CG”, 1)
u = TrialFunction(V)
v = TestFunction(V)

Define Dirichlet boundary conditions at top and bottom boundaries

bcs = [DirichletBC(V, 0.0,boundaries,2),
DirichletBC(V, 0.0, boundaries, 4),DirichletBC(V,0.0,boundaries,5),DirichletBC(V,0.0,boundaries,6)]

#interpolate initial condition
u_n = interpolate(u_0, V)

Define new measures associated with the interior domains and

exterior boundaries

ds = Measure(‘ds’, domain=mesh, subdomain_data=boundaries)
dx = Measure(‘dx’, domain=mesh)

Define variational form

a = uvdx + dtdot(grad(u), grad(v))dx
L = (u_n + dtf)vdx +g_Lvds(1)+g_Rv*ds(3)

Separate left and right hand sides of equation

u=Function(V)

file =File(“dfd.pvd”)
t = 0

T=50*dt

while (t<T):
# Update current time
t += dt

# Compute solution

solve(a == L, u, bcs)

# Update previous solution
u_n.assign(u)

file << (u,t)

Error [

Found no facets matching domain for boundary condition.

2

Please make sure that the code is encapsulated with 3x`
as follows

```python
def f(x):
    return x
```

In general I would start by increasing

to 1E-12 or 1E-13