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Volume 8, Issue 1
Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook

Achi Brandt, James Brannick, Karsten Kahl & Ira Livshits

DOI: 10.4208/nmtma.2015.w06si

Numer. Math. Theor. Meth. Appl., 8 (2015), pp. 112-135.

Published online: 2015-08

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  • Abstract

This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for computing accurate prolongation operators and the bootstrap cycles for computing the test vectors that are used in the least squares process. We review some recent research in the development, analysis and application of bootstrap algebraic multigrid and point to open problems in these areas. Results from our previous research as well as some new results for some model diffusion problems with highly oscillatory diffusion coefficient are presented to illustrate the basic components of the BAMG algorithm.

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@Article{NMTMA-8-112, author = {Achi Brandt, James Brannick, Karsten Kahl and Ira Livshits}, title = {Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2015}, volume = {8}, number = {1}, pages = {112--135}, abstract = {

This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for computing accurate prolongation operators and the bootstrap cycles for computing the test vectors that are used in the least squares process. We review some recent research in the development, analysis and application of bootstrap algebraic multigrid and point to open problems in these areas. Results from our previous research as well as some new results for some model diffusion problems with highly oscillatory diffusion coefficient are presented to illustrate the basic components of the BAMG algorithm.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2015.w06si}, url = {http://global-sci.org/intro/article_detail/nmtma/12402.html} }
TY - JOUR T1 - Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook AU - Achi Brandt, James Brannick, Karsten Kahl & Ira Livshits JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 112 EP - 135 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.w06si UR - https://global-sci.org/intro/article_detail/nmtma/12402.html KW - AB -

This paper provides an overview of the main ideas driving the bootstrap algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for computing accurate prolongation operators and the bootstrap cycles for computing the test vectors that are used in the least squares process. We review some recent research in the development, analysis and application of bootstrap algebraic multigrid and point to open problems in these areas. Results from our previous research as well as some new results for some model diffusion problems with highly oscillatory diffusion coefficient are presented to illustrate the basic components of the BAMG algorithm.

Achi Brandt, James Brannick, Karsten Kahl and Ira Livshits. (2015). Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook. Numerical Mathematics: Theory, Methods and Applications. 8 (1). 112-135. doi:10.4208/nmtma.2015.w06si
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