I have been having trouble solving a coupled set of PDEs in mathematica (electrical current flow), and the issue appears to be in the boundary conditions. Specifically, I have PDES as follows:
sum_{i} \partial_i J_i = 0 J_i = sum_{j} c_{ij} \partial_j phi
where i,j = x,y. On the boundary I need to specify values of J_i as hat{n} cdot J = 0, as well as two positions for source and drain where the current enters/exits.
Due to the complicated geometry I do not know how to specify hat{n} dot J = 0. Mathematica tutorials seem to only provide an example regarding the heat equation with a scalar field, instead of a two component vector field.
Any help would be appreciated, thanks!