Symmetric marching technique /SMT/ for the efficient solution of discretized Poisson equation on non-rectangular regions

Two methods for solving the discretized Poisson equation on nonrectangular regions are developed using the symmetric marching technique. Method I is found to cover all irregular geometries except for regions with holes, while method II, based on capacitance matrix, is shown to cover any irregular bounded region. Since the capacitance matrix depends only on the geometry of the problem and not on the boundary data, method II is especially suitable for problems of similar geometry. However, method I is significantly more efficient than method II. Numerical results are presented for the solutions of several model problems utilizing both of these methods.