Sparse matrix approximations for multigrid methods

Matthias Bolten; Thomas K. Huckle; Christos D. Kravvaritis

doi:10.1016/j.laa.2015.11.008

Sparse matrix approximations for multigrid methods

Matthias Bolten, Thomas K. Huckle, Christos D. Kravvaritis

Informatics 5 - Chair of Scientific Computing

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We discuss the application of sparse matrix approximations for two-grid and V-cycle multigrid methods. Sparse approximate inverses can be used as smoothers, further the Galerkin coarse matrix can be sparsified by sparse approximation techniques. Also the projection can be defined by combining sparse approximation with side conditions related to high frequency components. Numerical results are given, which demonstrate the efficiency and accuracy of the proposed strategies.

Original language	English
Pages (from-to)	58-76
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	502
DOIs	https://doi.org/10.1016/j.laa.2015.11.008
State	Published - 1 Aug 2016

Keywords

Generating functions
Multigrid
Sparse matrix approximations
Toeplitz matrices

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10.1016/j.laa.2015.11.008

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abstract = "We discuss the application of sparse matrix approximations for two-grid and V-cycle multigrid methods. Sparse approximate inverses can be used as smoothers, further the Galerkin coarse matrix can be sparsified by sparse approximation techniques. Also the projection can be defined by combining sparse approximation with side conditions related to high frequency components. Numerical results are given, which demonstrate the efficiency and accuracy of the proposed strategies.",

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AU - Bolten, Matthias

AU - Huckle, Thomas K.

AU - Kravvaritis, Christos D.

PY - 2016/8/1

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N2 - We discuss the application of sparse matrix approximations for two-grid and V-cycle multigrid methods. Sparse approximate inverses can be used as smoothers, further the Galerkin coarse matrix can be sparsified by sparse approximation techniques. Also the projection can be defined by combining sparse approximation with side conditions related to high frequency components. Numerical results are given, which demonstrate the efficiency and accuracy of the proposed strategies.

AB - We discuss the application of sparse matrix approximations for two-grid and V-cycle multigrid methods. Sparse approximate inverses can be used as smoothers, further the Galerkin coarse matrix can be sparsified by sparse approximation techniques. Also the projection can be defined by combining sparse approximation with side conditions related to high frequency components. Numerical results are given, which demonstrate the efficiency and accuracy of the proposed strategies.

KW - Generating functions

KW - Multigrid

KW - Sparse matrix approximations

KW - Toeplitz matrices

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DO - 10.1016/j.laa.2015.11.008

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VL - 502

SP - 58

EP - 76

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Sparse matrix approximations for multigrid methods

Abstract

Keywords

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