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Algorithmique et calculs de complexité pour un solveur de type dissections emboîtées. (Algorithmic study and complexity bounds for a nested dissection solver). (French) Zbl 0663.65020

We consider the nested dissection method based on separator theorems introduced by R. E. Tarjan [ibid. 50, 377-404 (1987; Zbl 0645.65012)] and the second author [ibid. 47, 175-190 (1985; Zbl 0537.65025)] used for solving large sparse systems of linear equations. More precisely, we study a block storage scheme such as proposed by A. George [SIAM J. Numer. Anal. 14, 161-179 (1977; Zbl 0356.65023)] for regular square grids and we prove the following results: first, for families of graphs of bounded degree with \(n^{\sigma}\)-separator theorem, \(1/2\leq \sigma <1\), the overhead storage of the block data structure for the factored matrix is linear in system dimension; on the other hand, by adding a non restrictive assumption on the separation, this structure can be constructed by a block symbolic factorization which runs in time linear in matrix dimension. Numerical experiments illustrating these theoretical results are provided.
Reviewer: P.Charrier

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65F50 Computational methods for sparse matrices
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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References:

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