Numerical solution of three-dimensional boundary-value problems by generalized approximate inverse matrix techniques

Abstract

Generalized Approximate Inverse Matrix (GAIM) techniques based on the concept of LU-type sparse factorization procedures are introduced for calculating explicitly approximate inverses of large sparse unsymmetric matrices of regular structure without inverting the factors L and U. Explicit first and second-order iterative methods in conjunction with modified forms of the GAIM techniques are presented for solving numerically three-dimensional initial/boundary-value problems on multiprocessor systems. Applications of the new methods on a 3D boundary-value problem is discussed and numerical results are given.

Keywords:

• Boundary-value problems
• unsymmetric systems
• approximate inverse matrix methods
• explicit difference equations
• preconditioning
• three-space variables