I am trying to solve a 1 Dimensional eigenvalue of poisson problem:
$$\nabla \phi ^2 +\nabla \phi = k\phi$$
with the boundary condition: $\phi (0)=0 , \nabla \phi(1) = 0 $.
I could solve this directly, but I am trying to solve it for parallel calculation framework by dividing the problems into 3 or 4 meshes. Then, I connect the middle boundary with the robin boundary condition and the most left mesh with the zero flux and robin boundary, and the most right mesh with robin boundary and right mesh.
When I solve this problem, I find an inconsistency problem when I vary the number of mesh divisions. Could you guys give me some insight?
To be more detail, actually i just try to do the simple implementation first to test whether my algorithm will work or not. So what i did is: let say i have 3 parallel meshes. Previously i only have 1 FEM main equation, now i will have 3 FEM Equation (each mesh will have their own governing equation), Then i connect my parallel mesh by using the robin boundary condition for the same interface. Is this okay?