EXPLICIT SEMIDIRECT METHODS BASED ON APPROXIMATE INVERSE MATRIX TECHNIQUES FOR SOLVING BOUNDARY-VALUE-PROBLEMS ON PARALLEL PROCESSORS

Generalized approximate inverse matrix techniques and sparse Gauss-Jordan elimination procedures based on the concept of sparse product form of the inverse are introduced for calculating explicitly approximate inverses of large sparse unsymmetric (n multiplied by n) matrices. Explicit first and second order semi-direct methods in conjunction with the derived approximate inverse matrix techniques are presented for solving Parabolic and Elliptic difference equations on parallel processors. Application of the new methods on a 2D-model problem is discussed and numerical results are given.