Computer simulation using particles
Computer simulation using particles
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
Journal of Computational Physics
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Journal of Computational Physics
A Cartesian grid embedded boundary method for hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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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 L"1 with respect to the grid resolution is demonstrated for both problems.