Explicit preconditioned methods for solving 3d boundary-value problems by approximate inverse finite element matrix techniques

Abstract

A new class of factorization algorithmic procedures and approximate inverse finite element matrix techniques for solving large symmetric matrices of irregular structure, without inverting the decomposition factors, are presented. Explicit preconditioned iterative methods, based on these approximate finite element inverse matrix techniques, are used for the efficient numerical solution of large linear systems resulting from the finite element discretization of boundary value problems in three space dimensions. Application of the new methods on a 3D linear boundary value problem is discussed and numerical results are given.