Sparse Approximate Inverse and Multilevel Block
ILU Preconditioning Techniques for General Sparse Matrices

Jun Zhang
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506--0046, USA


We investigate the use of sparse approximate inverse techniques in a multilevel block ILU preconditioner to design a robust and efficient parallelizable preconditioner for solving general sparse matrices. The resulting preconditioner retains robustness of the multilevel block ILU preconditioner (BILUM) and offers a new way to control the fill-in elements when large size blocks (subdomains) are used to form block independent set. Moreover, the new preconditioner affords maximum parallelism for operations within each level as well as for the coarsest level solution. Thus it has two advantages over the standard BILUM preconditioner: the ability to control sparsity and increased parallelism. Numerical experiments are used to show the effectiveness and efficiency of the new preconditioner.

Key words: Sparse matrices, incomplete LU factorization, multilevel ILU preconditioner, sparse approximate inverse, Krylov subspace methods.

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This paper has been published in Applied Numerical Mathematics, Vol. 35, No. 1, 67-86 (2000).
(Technical Report No. 279-98, Department of Computer Science, University of Kentucky, Lexington, KY, 1998.)
This research is supported in part by the University of Kentucky Center for Computational Sciences.