### 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 language | English (US) |
---|---|

Pages (from-to) | 612-632 |

Number of pages | 21 |

Journal | SIAM Journal on Scientific Computing |

Volume | 33 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2011 |

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### All Science Journal Classification (ASJC) codes

- Computational Mathematics
- Applied Mathematics

### Cite this

*SIAM Journal on Scientific Computing*,

*33*(2), 612-632. https://doi.org/10.1137/090752973

}

*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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bootstrap AMG

AU - Brandt, A.

AU - Brannick, J.

AU - Kahl, K.

AU - Livshits, I.

PY - 2011/6/1

Y1 - 2011/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79957581762&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957581762&partnerID=8YFLogxK

U2 - 10.1137/090752973

DO - 10.1137/090752973

M3 - Article

AN - SCOPUS:79957581762

VL - 33

SP - 612

EP - 632

JO - SIAM Journal of Scientific Computing

JF - SIAM Journal of Scientific Computing

SN - 1064-8275

IS - 2

ER -