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Sparse approximate inverse and multilevel block ILU preconditioning techniques for general sparse matrices. (English) Zbl 0966.65043

A preconditioning technique for general sparse matrices, which combines a multilevel block ILU (BILUM) with the sparse approximate inverse techniques, is presented.
The two basic methods are introduced and the resulting preconditioner is designed to have the ability of controlling sparsity and increased parallelism compared to the standard BILUM preconditioner. Extensive numerical experiments with a discretized convection-diffusion problem and five additional, well-known matrices from different sparse matrix collections illustrate the behaviour of the proposed preconditioner, but also the realization that it is unlikely that there exists a general purpose preconditioner being superior for all types of problems.

MSC:

65F35 Numerical computation of matrix norms, conditioning, scaling
65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
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