Parallel Two Level Block ILU Preconditioning
Techniques for Solving Large Sparse Linear Systems

Chi Shen and Jun Zhang
Laboratory for High Performance Scientific Computing and Numerical Simulation
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA

Abstract

We discuss issues related to domain decomposition and multilevel preconditioning techniques which are often employed for solving large sparse linear systems in parallel computations. We introduce a class of parallel preconditioning techniques for general sparse linear systems based on a two level block ILU factorization strategy. We give some new data structures and strategies to construct local coefficient matrix and local Schur complement matrix in each processor. The preconditioner constructed is fast and robust for solving certain large sparse matrices. Numerical experiments show that our domain based two level block ILU preconditioners are more robust and more efficient than some published ILU preconditioners based on Schur complement techniques for parallel sparse matrix solutions.

Key words: Parallel preconditioning, sparse matrices, Schur complement techniques, BILUTM, domain decomposition

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This paper has been published in Parallel Computing, Vol. 28, No. 10, pp. 1451-1475 (2002).

Technical Report No. 305-00, Department of Computer Science, University of Kentucky, Lexington, KY, 2000. The research work was supported in part by the U.S. National Science Foundation under grants CCR-9902022 and CCR-9988165, and in part by the University of Kentucky Center for Computational Sciences and the University of Kentucky College of Engineering.