Journal of Mathematical Modelling and Algorithms

, Volume 1, Issue 3, pp 181–192

Domain Decomposition–Finite Difference Approximate Inverse Preconditioned Schemes for Solving Fourth-Order Equations

  • George A. Gravvanis

DOI: 10.1023/A:1020538522302

Cite this article as:
Gravvanis, G.A. Journal of Mathematical Modelling and Algorithms (2002) 1: 181. doi:10.1023/A:1020538522302


A new class of explicit approximate inverse preconditioning is introduced for solving fourth-order equations, based on the ‘coupled equation approach’, by the domain decomposition method in conjunction with various finite difference approximation schemes. Explicit approximate inverse arrow-type matrix techniques, based on the concept of sparse LU-type factorization procedures, are introduced for computing a class of approximate inverses. Explicit preconditioned conjugate gradient-type schemes are presented for the efficient solution of linear systems. Applications of the method to a biharmonic problem are discussed and numerical results are given.

domain decomposition methodfinite difference methodbiharmonic equationsapproximate factorization procedureapproximate inverse matrix techniquespreconditioningparallel iterative methods

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • George A. Gravvanis
    • 1
  1. 1.Department of Information and Communication Systems EngineeringUniversity of the AegeanKarlovasi, SamosGreece