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Performance of ILU factorization preconditioners based on multisplittings. (English) Zbl 1040.65032

The author investigates the parallelizability of incomplete LU (ILU) preconditioners for sparse block tridiagonal H matrices. Preconditioned Krylov subspace methods are generally necessary to speed up convergence. But the ILU factorization does not lend itself to parallelization. However, if the multisplitting method converges, then \(P^{-1}\) (with \(PA = I-H\) and an iteration matrix \(H\) with spectral radius less than 1) is a good preconditioner for the Krylov method. Such a preconditioner \(P\) is derived from the multisplitting of the block diagonal H-matrix and it can be used in parallel in the preconditioner solver step to advantage. The convergence of such a scheme is studied, as well as the parallel performance for the ILU preconditioned BiCGSTAB algorithm.

MSC:

65F10 Iterative numerical methods for linear systems
65F50 Computational methods for sparse matrices
65F35 Numerical computation of matrix norms, conditioning, scaling
65Y05 Parallel numerical computation
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