A MODIFIED STRONGLY IMPLICIT PROCEDURE FOR THE NUMERICAL SOLUTION OF FIELD PROBLEMS

Abstract

A modified strongly implicit procedure for solving the system of algebraic equations that arise in the finite-difference or finite-analytic description of field problems is presented. The method is derived for a nine-point difference scheme and can readily be applied to the more conventional five-point scheme simply through the use of the five-point scheme coefficients. The method is demonstrated by application to several examples and a comparison is made between the performance of the modified procedure and that of the strongly implicit procedure, the alternating direction implicit method, and successive over-relaxation. In all cases examined the modified strongly implicit procedure offers superior results when the number of iterations required for convergence or the computational cost required for convergence is used as the measure of performance. The method is also less sensitive to control volume aspect ratio, relaxation parameters, and mesh subdivision than other available procedures. Savings in computational cost for a converged solution range from a factor of two to a factor of four over the strongly implicit procedure. It is felt that the development of this procedure offers a significant advance in the state of the art of solving the finite-difference equations that are used to describe field problems.