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Volume 34, Issue 5
Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media

Yu Du & Haijun Wu

DOI: 10.4208/cicp.OA-2023-0032

Commun. Comput. Phys., 34 (2023), pp. 1247-1276.

Published online: 2023-12

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  • Abstract

We extend the pure source transfer domain decomposition method (PSTDDM) to solve the perfectly matched layer approximation of Helmholtz scattering problems in heterogeneous media. We first propose some new source transfer operators, and then introduce the layer-wise and block-wise PSTDDMs based on these operators. In particular, it is proved that the solution obtained by the layer-wise PSTDDM in $\mathbb{R}^2$ coincides with the exact solution to the heterogeneous Helmholtz problem in the computational domain. Second, we propose the iterative layer-wise and block-wise PSTDDMs, which are designed by simply iterating the PSTDDM alternatively over two staggered decompositions of the computational domain. Finally, extensive numerical tests in two and three dimensions show that, as the preconditioner for the GMRES method, the iterative PSTDDMs are more robust and efficient than PSTDDMs for solving heterogeneous Helmholtz problems.

  • Keywords

Helmholtz equation, large wave number, perfectly matched layer, source transfer, domain decomposition method, preconditioner, heterogeneous problem.

  • AMS Subject Headings

65N55, 65F10, 65F08, 65Y05, 65Y20, 65N30, 78A40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-34-1247, author = {Du , Yu and Wu , Haijun}, title = {Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media}, journal = {Communications in Computational Physics}, year = {2023}, volume = {34}, number = {5}, pages = {1247--1276}, abstract = {

We extend the pure source transfer domain decomposition method (PSTDDM) to solve the perfectly matched layer approximation of Helmholtz scattering problems in heterogeneous media. We first propose some new source transfer operators, and then introduce the layer-wise and block-wise PSTDDMs based on these operators. In particular, it is proved that the solution obtained by the layer-wise PSTDDM in $\mathbb{R}^2$ coincides with the exact solution to the heterogeneous Helmholtz problem in the computational domain. Second, we propose the iterative layer-wise and block-wise PSTDDMs, which are designed by simply iterating the PSTDDM alternatively over two staggered decompositions of the computational domain. Finally, extensive numerical tests in two and three dimensions show that, as the preconditioner for the GMRES method, the iterative PSTDDMs are more robust and efficient than PSTDDMs for solving heterogeneous Helmholtz problems.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2023-0032}, url = {http://global-sci.org/intro/article_detail/cicp/22213.html} }
TY - JOUR T1 - Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media AU - Du , Yu AU - Wu , Haijun JO - Communications in Computational Physics VL - 5 SP - 1247 EP - 1276 PY - 2023 DA - 2023/12 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2023-0032 UR - https://global-sci.org/intro/article_detail/cicp/22213.html KW - Helmholtz equation, large wave number, perfectly matched layer, source transfer, domain decomposition method, preconditioner, heterogeneous problem. AB -

We extend the pure source transfer domain decomposition method (PSTDDM) to solve the perfectly matched layer approximation of Helmholtz scattering problems in heterogeneous media. We first propose some new source transfer operators, and then introduce the layer-wise and block-wise PSTDDMs based on these operators. In particular, it is proved that the solution obtained by the layer-wise PSTDDM in $\mathbb{R}^2$ coincides with the exact solution to the heterogeneous Helmholtz problem in the computational domain. Second, we propose the iterative layer-wise and block-wise PSTDDMs, which are designed by simply iterating the PSTDDM alternatively over two staggered decompositions of the computational domain. Finally, extensive numerical tests in two and three dimensions show that, as the preconditioner for the GMRES method, the iterative PSTDDMs are more robust and efficient than PSTDDMs for solving heterogeneous Helmholtz problems.

Yu Du & Haijun Wu. (2023). Iterative Pure Source Transfer Domain Decomposition Methods for Helmholtz Equations in Heterogeneous Media. Communications in Computational Physics. 34 (5). 1247-1276. doi:10.4208/cicp.OA-2023-0032
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