Solving large sparse finite element systems of nonlinear equations by explicit semi-direct methods based on approximate inverse preconditioners

  • Elias A. Lipitakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1225)


A class of generalized sparse approximate inverse preconditioners, based on the concept of adaptable incomplete LU-type decomposition, is presented. Explicit preconditioned semi-direct methods in conjuction with modified forms of Newton/Picard methods are used for solving nonlinear initial/boundary value problems. The applicability, effectiveness and performance of the proposed hybrid iterative schemes and sparse approximate inverse preconditioners is discussed and numerical results for solving characteristic nonlinear elliptic PDE's are given.


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  1. [1]
    LIPITAKIS E.A.(1984): Generalized EL sparse factorization techniques for solving unsymmetric FE svstems, Computing 32, 255–270.Google Scholar
  2. [2]
    LIPITAKIS E.A., GRAVVANIS G.A. (1995): Explicit precond. iterative methods for solving large unsymmetric FE systems, Computing 54, 167–183.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Elias A. Lipitakis
    • 1
  1. 1.Department of InformaticsAthens University of Economics and BusinessAthensGreece

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