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

The basic error vector propagation method EVP for the solution of elliptic equations is described. Its advantages and limitations are compared to other direct solvers and iterative methods. A new technique called stabilized error vector propagation SEVP is presented. This method has most of the advantages of the EVP algorithm and, in addition, it is stable for all grid sizes. By solving Poissons equation with Dirichlet boundary conditions, SEVP is found to be 3 to 10 times faster than competative direct methods on a vector computer and requires an order of magnitude smaller computer memory. SEVP is at least 10 times faster than SOR. The efficiency of the SEVP method is found to increase for grids stretched in the marching direction while other methods tend to deteriorate under similar conditions. Author