Polynomial preconditioners based on factorized sparse approximate inverses

Authors:
J. Cerdán;J. Marín;A. Martínez
Affiliations:
Departament de Matemàtica Aplicada, Universitat Politècnica de València, 46071 València, Spain;Department of Applied Mathematics, ESTIA, Universidad Politechnica de Valenci, Camino de Vera 14, 46002 Valencia, Spain;Dipartamento di Metodi e Modelli Matematici per le Scienze Applicate, Universitá di Padova. Via Belzoni, 7 Padova, Italy
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

Let Ax = b be a linear system where A is a symmetric positive definite matrix. An additive polynomial preconditioner for the Conjugate Gradient method based on multisplittings is proposed. The multisplittings are obtained by computing some factorized sparse approximate inverses of the coefficient matrix. Namely, splittings of the form A = (ZZT)-1 -N, ZZT ≈ A-1 induced by the AINV and FSAI factorized approximate inverse preconditioners applied to diagonal blocks of A are used. The applicability of this preconditioner is studied. Moreover, the results of the numerical experiments obtained on a Cray T3E for a representative set of matrices are presented. Specifically, structural analysis and transport/diffusion problems are considered. The effect of the Reverse Cuthill-McKee (RCM) and Multiple Minimum Degree (MMD) orderings is evaluated.