A Multidimensional Compact Higher-Order Scheme for 3-D Poisson's Equation

Abstract A multidimensional compact finite-difference scheme is applied to the solution of a three-dimensional Poisson's equation. Excellent precision is obtained by means of a moderate discretization net. The presence of Neumann boundary conditions calls for special attention because these normal conditions affect the global precision. The numerical results for a test case involving five Neumann conditions and one Dirichlet condition on the six faces of a unit cube show good agreement with the analytical solution.