Numerical Solution of Elliptic Differential Equations by Reduction to the Interface

Boris N. Khoromskij, Gabriel Wittum - Collection Lecture Notes in Computational Science and Engineering

295 pages, parution le 25/02/2004

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Résumé

This is the first book that deals systematically with the numerical solution of elliptic partial differential equations by their reduction to the interface via the Schur complement.Inheriting the beneficial features of finite element, boundary element and domain decomposition methods, our approach permits solving iteratively the Schur complement equation with linear-logarithmic cost in the number of the interface degrees of freedom. The book presents the detailed analysis of the efficient data-sparse approximation techniques to the nonlocal Poincaré-Steklov interface operators associated with the Laplace, biharmonic, Stokes and Lamé equations. Another attractive topic are the robust preconditioning methods for elliptic equations with highly jumping, anisotropic coefficients. A special feature of the book is a unified presentation of the traditional iterative substructuring and multilevel methods combined with modern matrix compression techniques applied to the Schur complement on the interface.

Written for:
Graduate students, researchers

Sommaire

Finite element method for elliptic PDEs
Elliptic Poincarré-Steklov operators
Iterative substructuring methods
Multilevel methods
Robust preconditioners for equations with jumping anisotropic coefficients
Frequency filtering techniques
Data-sparse approximation to the Schur complement for laplacian
Discrete Poincarré-Steklov mappings for biharmonic and Lamé equations
Interface reduction for the stokes equation
References
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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Boris N. Khoromskij, Gabriel Wittum
Collection	Lecture Notes in Computational Science and Engineering
Parution	25/02/2004
Nb. de pages	295
Format	15,5 x 23,5
Couverture	Broché
Poids	470g
Intérieur	Noir et Blanc
EAN13	9783540204060