Modified block-approximate factorization strategies

Two variants of modified incomplete block-matrix factorization with additive correction are proposed for the iterative solution of large linear systems of equations. Both rigorous theoretical support and numerical evidence are given displaying their efficiency when applied to discrete second order partial differential equations (PDEs), even in the case of quasi-singular problems. © 1992 Springer-Verlag.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Conditioning analysis of sparse block approximate factorizations

The conditioning analysis of sparse approximate block factorizations of Stieltjes matrices developed by Beauwens and Ben Bouzid in [10] is generalized here on the basis of recent improvements of the point factorization analysis. In particular, the scope of the O(h-1) bound previously obtained for a specific class of applications to discrete multidimensional elliptic partial differential equations is substantially extended. © 1991.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Sparse approximate block factorizations for solving symmetric positive (semi)definite linear systems

Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Performance of parallel incomplete LDLt factorizations for solving acoustic wave propagation problems from industry

Parallel incomplete LDLt (ParILDLt) factorizations are used to solve highly indefinite complex-symmetric linear systems that arise from finite element discretization of acoustic wave propagation problems. The parallelization strategy is a generalized domain decomposition type approach in which adjacent subdomains have to exchange data during the construction of the incomplete factorization preconditioning matrix, as well as during each local forward and backward substitution. Comparison with the SYSNOISE (LMS International NV) direct solver, and the finite element tearing and interconnecting method for the Helmholtz equation (FETI-H), is done in terms of execution time and memory usage. Challenging industrial problems are tested, showing that high performance is achieved with ParlLDLt. Copyright © 2004 John Wiley & Sons, Ltd.SCOPUS: ar.jFLWINinfo:eu-repo/semantics/publishe

Taking advantage of the potentialities of dynamically modified block incomplete factorizations

Recently, modified block incomplete factorizations with dynamic diagonal perturbations have been introduced as preconditioning techniques to solve large linear systems, and were successfully tested on isotropic and moderately anisotropic two-dimensional partial differential equations (PDEs). An analytic study is performed on the basis of improved versions of results published elsewhere, displaying why dynamic methods should be preferred to standard block methods; in particular the empirical observation that the optimal choice of the involved parameter does not significantly vary from one problem to another is theoretically confirmed. It is also explained why, in the case of strong anisotropy, lack of attention when adding diagonal perturbations may result in very poor performance. Rules to surmount this inconvenience are discussed and tested on discretized two-dimensional PDEs.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Lower eigenvalue bounds for singular pencils of matrices

Beauwens' procedure for obtaining lower eigenvalue bounds for (regular) pencils of matrices A-γB is simplified and extended to the singular case. The theory is then compared, through a particular perturbed modified incomplete factorization, with Notay's generalization of another approach, initiated by Gustafsson, and developed by Axelsson and Barker and by Wilmet. © 1992.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Implementation of parallel block preconditionings on a transputer-based multiprocessor

In this paper we are concerned with the implementation on distributed memory MIMD computers of parallel block preconditionings for solving large and sparse symmetric positive definite linear systems. For this purpose, a recently proposed ordering strategy is used. Experimental tests performed on a transputer-based multiprocessor computer are reported, displaying that good performance can be achieved in exchange for some optimization effort and on to the assumption that the number of processors is smaller by orders of magnitude than the size of the problem to solve, which agrees with observations made elsewhere. © 1995.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Dynamically Relaxed Block Incomplete Factorizations For Solving Two- And Three-Dimensional Problems

. To efficiently solve second order discrete elliptic PDEs, by Krylov subspace like methods, one needs to use some robust preconditioning techniques. Relaxed incompletefactorizations (RILU) are powerful candidates. Unfortunately, their efficiency critically depends on the choice of the relaxation parameter ! whose "optimal" value is not only hard to estimate, but also strongly varies from a problem to another. These methods interpolate between the popular ILU and its modified variant MILU. Concerning the pointwise schemes, a new variant of RILU that dynamically computes variable ! = ! i has been introduced recently. Like its ancestor RILU and unlike standard methods, it is robust with respect to both existence and performance. On top of that, it breaks the problem-dependence of "!opt ". A block version of this dynamically relaxed method is proposed, and compared with classical pointwise and blockwise methods as well as with some existing "dynamic" variants. Key words. Discretized part..