Filtering algebraic multigrid and adaptive strategies

Arne Nägel; Robert D. Falgout; Gabriel Wittum

doi:10.1007/s00791-007-0066-9

Filtering algebraic multigrid and adaptive strategies

Arne Nägel^*, Robert D. Falgout, Gabriel Wittum

^*Corresponding author for this work

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

11 Scopus citations

Abstract

Solving linear systems arising from partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. It is shown, how the class of filtering multigrid methods can be integrated into an adaptive, self-correcting framework. Numerical experiments, which are performed for a class of scaled operators, underline the results.

Original language	English (US)
Pages (from-to)	159-167
Number of pages	9
Journal	Computing and Visualization in Science
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/s00791-007-0066-9
State	Published - May 2008
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgments The authors are indebted to Christian Wagner for sharing his source code and contributing to this article. For Falgout: This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

ASJC Scopus subject areas

Theoretical Computer Science
Software
Modeling and Simulation
General Engineering
Computer Vision and Pattern Recognition
Computational Theory and Mathematics

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10.1007/s00791-007-0066-9

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abstract = "Solving linear systems arising from partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. It is shown, how the class of filtering multigrid methods can be integrated into an adaptive, self-correcting framework. Numerical experiments, which are performed for a class of scaled operators, underline the results.",

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note = "Funding Information: Acknowledgments The authors are indebted to Christian Wagner for sharing his source code and contributing to this article. For Falgout: This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.",

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AU - Wittum, Gabriel

N1 - Funding Information: Acknowledgments The authors are indebted to Christian Wagner for sharing his source code and contributing to this article. For Falgout: This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48.

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AB - Solving linear systems arising from partial differential equations, multigrid and multilevel methods have proven optimal complexity and efficiency properties. Due to shortcomings of geometric approaches, algebraic multigrid methods have been developed. One example is the filtering algebraic multigrid method introduced by C. Wagner. This paper proposes a variant of Wagner's method with substantially improved robustness properties. It is shown, how the class of filtering multigrid methods can be integrated into an adaptive, self-correcting framework. Numerical experiments, which are performed for a class of scaled operators, underline the results.

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ER -

Filtering algebraic multigrid and adaptive strategies

Abstract

Bibliographical note

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