An iterative boundary potential method for the infinite domain Poisson problem with interior Dirichlet boundaries

An iterative method is developed for the solution of Poisson’s problem on an infinite domain in the presence of interior boundaries held at fixed potential, in three dimensions. The method combines pre-existing fast multigrid-based Poisson solvers for data represented on Cartesian grids with the fast multipole method. Interior boundaries are represented with the embedded boundary formalism. The implementation is in parallel and uses adaptive mesh refinement. Examples are presented for a smooth interior boundary for which an analytical result is known, and for an irregular interior boundary problem. Second-order accuracy in L1L1 with respect to the grid resolution is demonstrated for both problems.