Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems /

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 comput...

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Principais autores: Bebendorf, Mario., SpringerLink (Online service)
Formato: Digital
Publicado em:
Assuntos:
Matrizes (Matemática).
Equações diferenciais parciais.
Análise numérica.
Computação -
Matemática.
Endereço do item:http://dx.doi.org/10.1007/978-3-540-77147-0
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spelling oai:localhost:123456789-1297942023-07-17T15:13:12Z Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems / Bebendorf, Mario. SpringerLink (Online service) Matrizes (Matemática). Equações diferenciais parciais. Análise numérica. Computação - Matemática. Matemática. 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. 0 2022-10-06T07:51:11Z 2022-10-06T07:51:11Z 2008. Digital 512.643 B387h 9783540771470 197811 http://dx.doi.org/10.1007/978-3-540-77147-0 http://dx.doi.org/10.1007/978-3-540-77147-0
institution Acervo SISBI
collection SIGAA
topic Matrizes (Matemática).
Equações diferenciais parciais.
Análise numérica.
Computação -
Matemática.
Matemática.
spellingShingle Matrizes (Matemática).
Equações diferenciais parciais.
Análise numérica.
Computação -
Matemática.
Matemática.
Bebendorf, Mario.
SpringerLink (Online service)
Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems /
description 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.
format Digital
author Bebendorf, Mario.
SpringerLink (Online service)
author_facet Bebendorf, Mario.
SpringerLink (Online service)
author_sort Bebendorf, Mario.
title Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems /
title_short Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems /
title_full Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems /
title_fullStr Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems /
title_full_unstemmed Hierarchical Matrices A Means to Efficiently Solve Elliptic Boundary Value Problems /
title_sort hierarchical matrices a means to efficiently solve elliptic boundary value problems /
publishDate 2022
url http://dx.doi.org/10.1007/978-3-540-77147-0
work_keys_str_mv AT bebendorfmario hierarchicalmatricesameanstoefficientlysolveellipticboundaryvalueproblems
AT springerlinkonlineservice hierarchicalmatricesameanstoefficientlysolveellipticboundaryvalueproblems
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