Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems Mario Bebendorf

ISBN: 9783540771463

Published: June 13th 2008

Paperback

290 pages


Description

Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems  by  Mario Bebendorf

Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems by Mario Bebendorf
June 13th 2008 | Paperback | PDF, EPUB, FB2, DjVu, talking book, mp3, ZIP | 290 pages | ISBN: 9783540771463 | 10.68 Mb

Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices,MoreHierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way.

Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients. Furthermore, it presents in full detail the adaptive cross approximation method for the efficient treatment of integral operators with non-local kernel functions. The theory is supported by many numerical experiments from real applications.



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