Hierarchical matrices : a means to efficiently solve elliptic boundary value problems / Mario Bebendorf.

Format:

Book

Author/Creator:

Bebendorf, Mario.

Series:

Lecture notes in computational science and engineering ; 63.

Lecture notes in computational science and engineering, 1439-7358 ; 63

Language:

English

Subjects (All):

Matrices.

Boundary value problems.

Differential equations, Elliptic.

Physical Description:

1 online resource (304 p.)

Edition:

1st ed. 2008.

Place of Publication:

Berlin : Springer, 2008.

Language Note:

English

Summary:

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, 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.

Contents:

Low-Rank Matrices and Matrix Partitioning

Hierarchical Matrices

Approximation of Discrete Integral Operators

Application to Finite Element Discretizations.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611512798

9781281512796

1281512796

9783540771470

3540771476

OCLC:

272312980