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On block triangular preconditioned iteration methods for solving the Helmholtz equation. (English) Zbl 1433.65052

Summary: 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.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65F10 Iterative numerical methods for linear systems
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F08 Preconditioners for iterative methods

Software:

AILU
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Full Text: DOI

References:

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