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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!

Rain
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    Probably better to move this question to https://mathematica.stackexchange.com. It's probably off-topic here, the question seems to be more about correctly formulating the maths than about 'programming'. – High Performance Mark Mar 25 '23 at 11:51
  • This is an example of a Neumann boundary condition. You want to specify the flux on a boundary. There are lots of examples of how to do it for heat transfer problems. – duffymo Mar 28 '23 at 00:38

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