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Volume 6, Issue 3
A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions

Zhiming Chen & Xueshuang Xiang

DOI: 10.4208/nmtma.2013.1217nm

Numer. Math. Theor. Meth. Appl., 6 (2013), pp. 538-555.

Published online: 2013-06

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  • Abstract

In this paper we extend the source transfer domain decomposition method (STDDM) introduced by the authors to solve the Helmholtz problems in two-layered media, the Helmholtz scattering problems with bounded scatterer, and Helmholtz problems in 3D unbounded domains. The STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two layers. The details of STDDM is given for each extension. Numerical results are presented to demonstrate the efficiency of STDDM as a preconditioner for solving the discretization problem of the Helmholtz problems considered in the paper.

  • Keywords

Helmholtz equation, high frequency waves, PML, source transfer.

  • AMS Subject Headings

65F08, 65N55, 65Y20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-6-538, author = {Zhiming Chen and Xueshuang Xiang}, title = {A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2013}, volume = {6}, number = {3}, pages = {538--555}, abstract = {

In this paper we extend the source transfer domain decomposition method (STDDM) introduced by the authors to solve the Helmholtz problems in two-layered media, the Helmholtz scattering problems with bounded scatterer, and Helmholtz problems in 3D unbounded domains. The STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two layers. The details of STDDM is given for each extension. Numerical results are presented to demonstrate the efficiency of STDDM as a preconditioner for solving the discretization problem of the Helmholtz problems considered in the paper.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2013.1217nm}, url = {http://global-sci.org/intro/article_detail/nmtma/5917.html} }
TY - JOUR T1 - A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions AU - Zhiming Chen & Xueshuang Xiang JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 538 EP - 555 PY - 2013 DA - 2013/06 SN - 6 DO - http://doi.org/10.4208/nmtma.2013.1217nm UR - https://global-sci.org/intro/article_detail/nmtma/5917.html KW - Helmholtz equation, high frequency waves, PML, source transfer. AB -

In this paper we extend the source transfer domain decomposition method (STDDM) introduced by the authors to solve the Helmholtz problems in two-layered media, the Helmholtz scattering problems with bounded scatterer, and Helmholtz problems in 3D unbounded domains. The STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two layers. The details of STDDM is given for each extension. Numerical results are presented to demonstrate the efficiency of STDDM as a preconditioner for solving the discretization problem of the Helmholtz problems considered in the paper.

Zhiming Chen and Xueshuang Xiang. (2013). A Source Transfer Domain Decomposition Method for Helmholtz Equations in Unbounded Domain Part II: Extensions. Numerical Mathematics: Theory, Methods and Applications. 6 (3). 538-555. doi:10.4208/nmtma.2013.1217nm
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