Interpolation matrix with non matching meshes

Linear Algebra
15

My function works the same of the following:

but here the FunctionSpaces come from two different meshes.
Suppose that we want to interpolate a function from V_0 to V_1. It results:

\mathbf{I} = f(V_1, V_0)

Now, suppose that we have the following situation:

V_0 = FunctionSpace(mesh_0,("CG",deg_0))
V_1 = FunctionSpace(mesh_1,("CG",deg_1))

p_0 = Function(V_0)
...
p_0 = SomeComputations()

we define a new function on V_1:

p_1 = Function(V_1)

If we wanted to interpolate the function, we could use the command:

p_1.interpolate(p_0)

But now we have an alternative. We can indeed compute the interpolation matrix and compute the p_1 array from a matrix multiplication between I_matrix and the p_0 array:

I_matrix = interpolation_matrix_nonmatching_meshes(V_1,V_0)
p_1.x.array[:] = np.matmul(I_matrix,p_0.x.array)

getting the same result.

The purpose of such matrix is to try building a monolithic coupled vibro-acoustic system where the domains meshes at the interface don’t match.

Maybe someone else finds this useful.

Bye guys, I need a beer now.

Antonio

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