An Efficient Direct Solver for Separable and Non-Separable Elliptic Equations

Abstract

A new method for the numerical solution of elliptic difference equations called stabilized error vector propagation (SEVP) is derived. This method has most of the advantages of the error vector propagation algorithm and, in addition, is stable for all grid sizes. By solving Poisson's equation with Dirichlet boundary conditions, SEVP is found to be 3 to 10 times faster than competitive direct methods on a vector computer and requires an order of magnitude smaller computer memory. SEVP is at least 10 times faster than successive overrelaxation. Applications of this method to algorithms using both five- and nine- point stencils as well as stretched grids are discussed.