Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 367909, 12 pages.

Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations

Dandan Chen, Ting-Zhu Huang, and Liang Li

Full-text: Open access

Abstract

An algebraic multigrid (AMG) with aggregation technique to coarsen is applied to construct a better preconditioner for solving Helmholtz equations in this paper. The solution process consists of constructing the preconditioner by AMG and solving the preconditioned Helmholtz problems by Krylov subspace methods. In the setup process of AMG, we employ the double pairwise aggregation (DPA) scheme firstly proposed by Y. Notay (2006) as the coarsening method. We compare it with the smoothed aggregation algebraic multigrid and meanwhile show shifted Laplacian preconditioners. According to numerical results, we find that DPA algorithm is a good choice in AMG for Helmholtz equations in reducing time and memory. Spectral estimation of system preconditioned by the three methods and the influence of second-order and fourth-order accurate discretizations on the three techniques are also considered.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 367909, 12 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357179949

Digital Object Identifier
doi:10.1155/2012/367909

Mathematical Reviews number (MathSciNet)
MR2910911

Zentralblatt MATH identifier
1244.65044

Citation

Chen, Dandan; Huang, Ting-Zhu; Li, Liang. Comparison of Algebraic Multigrid Preconditioners for Solving Helmholtz Equations. J. Appl. Math. 2012, Special Issue (2012), Article ID 367909, 12 pages. doi:10.1155/2012/367909. https://projecteuclid.org/euclid.jam/1357179949


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