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Numerical Solution of Elliptic Differential Equations by Reduction to the Interface : Lecture Notes in Computational Science and Engineering, - Boris N. Khoromskij

Numerical Solution of Elliptic Differential Equations by Reduction to the Interface

Lecture Notes in Computational Science and Engineering,

Paperback Published: 9th February 2004
ISBN: 9783540204060
Number Of Pages: 293

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During the last decade essential progress has been achieved in the analysis and implementation of multilevel/rnultigrid and domain decomposition methods to explore a variety of real world applications. An important trend in mod­ ern numerical simulations is the quick improvement of computer technology that leads to the well known paradigm (see, e. g. , [78,179]): high-performance computers make it indispensable to use numerical methods of almost linear complexity in the problem size N, to maintain an adequate scaling between the computing time and improved computer facilities as N increases. In the h-version of the finite element method (FEM), the multigrid iteration real­ izes an O(N) solver for elliptic differential equations in a domain n c IRd d with N = O(h- ) , where h is the mesh parameter. In the boundary ele­ ment method (BEM) , the traditional panel clustering, fast multi-pole and wavelet based methods as well as the modern hierarchical matrix techniques are known to provide the data-sparse approximations to the arising fully populated stiffness matrices with almost linear cost O(Nr log?Nr), where 1 d Nr = O(h - ) is the number of degrees of freedom associated with the boundary. The aim of this book is to introduce a wider audience to the use of a new class of efficient numerical methods of almost linear complexity for solving elliptic partial differential equations (PDEs) based on their reduction to the interface.

Finite element method for elliptic PDEsp. 1
Elliptic Poincare-Steklov operatorsp. 37
Iterative substructuring methodsp. 63
Multilevel methodsp. 83
Robust preconditioners for equations with jumping anisotropic coefficientsp. 97
Frequency filtering techniquesp. 125
Data-sparse approximation to the Schur complement for Laplacianp. 161
Discrete Poincare-Steklov mappings for Biharmonic and lame equationsp. 189
Interface reduction for the stokes equationp. 209
Referencesp. 279
Indexp. 289
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783540204060
ISBN-10: 3540204067
Series: Lecture Notes in Computational Science and Engineering,
Audience: General
Format: Paperback
Language: English
Number Of Pages: 293
Published: 9th February 2004
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.68
Weight (kg): 0.45