On block triangular preconditioned iteration methods for solving the Helmholtz equation

Chao Lang, Rong Gao and Chujun Qiu

Applied Mathematics and Computation, 2020, vol. 369, issue C

Abstract: To further improve the efficiency of solving the Helmholtz equation in heterogeneous media with large wavenumber, the Krylov subspace methods incorporated with a class of inexact rotated block triangular preconditioners are presented to solve a block two-by-two linear system derived from the discrete Helmholtz equation. We further develop the eigenvalue properties of the preconditioned matrices to discuss the convergence of the corresponding preconditioned iteration methods. The superiority of such preconditioned iteration methods is prominent according to the numerical results when comparing with other classical iteration methods. We also investigate how the wavenumber influences the performance of the corresponding methods and it is shown that the iteration number of our proposed methods linearly increase with the wavenumber, roughly. Furthermore, the computational wave-fields which conform the real physical law are exhibited to show the correctness of our proposed numerical modeling algorithm.

Keywords: Helmholtz equation; Block two-by-two matrix; Block triangular preconditioning; Incomplete factorization (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319306873

DOI: 10.1016/j.amc.2019.124695

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