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Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook

Published online by Cambridge University Press:  03 March 2015

Achi Brandt ,
James Brannick ,
Karsten Kahl  and
Ira Livshits
Achi Brandt
Affiliation:
Department of Applied Mathematics & Computer Science, The Weizmann Institute of Science, 76100 Rehovot, Israel
James Brannick*
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA
Karsten Kahl
Affiliation:
Department of Mathematics, University of Wuppertal, Wuppertal, Germany
Ira Livshits
Affiliation:
Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA
*
*Email addresses: [email protected] (A. Brandt), [email protected] (J. Brannick), [email protected] (K. Kahl), [email protected] (I. Livshits)
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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.

Keywords

65F1065N2265N55Bootstrap algebraic multigridcompatible relaxationalgebraic distanceleast squares interpolation
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 1 , February 2015 , pp. 112 - 135
Copyright
Copyright © Global-Science Press 2015 

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