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Calculs de complexité relatifs à une méthode de dissection emboîtée. (French) Zbl 0537.65025

A ”nested dissection” ordering is given for solving any system of linear equations \(A\cdot X=B\) for the family of sparse symmetric positive definite matrices corresponding to the class of graphs of bounded degree whose subgraphs satisfy a \(\sqrt{n}\)-separator theorem, and we prove O(n.log(n)) fill and \(O(n\sqrt{n})\) operation count bounds. Then, the general implementation scheme in the finite element package MODULEF, for two-dimensional finite element problems, is presented, and some numerical results are given.

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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