Bootstrap AMG

A. Brandt, J. Brannick, K. Kahl, I. Livshits

Research output: Contribution to journalArticle

49 Citations (Scopus)

Abstract

We develop an algebraic multigrid (AMG) se tup scheme based on the bootstrap framework for multiscale scientific computation. Our approach uses a weighted least squares definition of interpolation, based on a set of test vectors that are computed by a bootstrap setup cycle and then improved by a multigrid eigensolver and a local residual-based adaptive relaxation process. To emphasize the robustness, efficiency, and flexibility of the individual components of the proposed approach, we include extensive numerical results of the method applied to scalar elliptic partial differential equations discretized on structured meshes. As a first test problem, we consider the Laplace equation discretized on a uniform quadrilateral mesh, a problem for which multigrid is well understood. Then, we consider various more challenging variable coefficient systems coming from covariant finite-difference approximations of the two-dimensional gauge Laplacian system, a commonly used model problem in AMG algorithm development for linear systems arising in lattice field theory computations.

Original languageEnglish (US)
Pages (from-to)612-632
Number of pages21
JournalSIAM Journal on Scientific Computing
Volume33
Issue number2
DOIs
StatePublished - Jun 1 2011

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Computation theory
Algebraic multigrid
Laplace equation
Relaxation processes
Bootstrap
Partial differential equations
Gages
Linear systems
Interpolation
Quadrilateral Mesh
Lattice Theory
Finite Difference Approximation
Weighted Least Squares
Elliptic Partial Differential Equations
Laplace's equation
Variable Coefficients
Field Theory
Test Problems
Gauge
Interpolate

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

Brandt, A., Brannick, J., Kahl, K., & Livshits, I. (2011). Bootstrap AMG. SIAM Journal on Scientific Computing, 33(2), 612-632. https://doi.org/10.1137/090752973
Brandt, A. ; Brannick, J. ; Kahl, K. ; Livshits, I. / Bootstrap AMG. In: SIAM Journal on Scientific Computing. 2011 ; Vol. 33, No. 2. pp. 612-632.
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Brandt, A, Brannick, J, Kahl, K & Livshits, I 2011, 'Bootstrap AMG', SIAM Journal on Scientific Computing, vol. 33, no. 2, pp. 612-632. https://doi.org/10.1137/090752973

Bootstrap AMG. / Brandt, A.; Brannick, J.; Kahl, K.; Livshits, I.

In: SIAM Journal on Scientific Computing, Vol. 33, No. 2, 01.06.2011, p. 612-632.

Research output: Contribution to journalArticle

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