I'm trying to solve a Poisson equation on a rectangular domain which ends up being a linear problem like Ax=b but since I know the boundary conditions, there are nodes where I have the solution values. I guess my question is... How can I solve the sparse system Ax=b if I know what some of the coordinates of x are and the undetermined values depend on these as well? It's the same as a normal solve except I know some of the solution to begin with.
Thanks!