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Volume 5, Issue 4
The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number

Wen Chen, Ji Lin & C. S. Chen

DOI: 10.4208/aamm.13-13S04

Adv. Appl. Math. Mech., 5 (2013), pp. 477-493.

Published online: 2013-08

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  • Abstract

In this paper, we investigate the method of fundamental solutions (MFS) for solving exterior Helmholtz problems with high wave-number in axisymmetric domains. Since the coefficient matrix in the linear system resulting from the MFS approximation has a block circulant structure, it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space. Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains.

  • Keywords

Method of fundamental solutions, exterior Helmholtz problem, circulant matrix, fast Fourier transform, axisymmetric domain.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-5-477, author = {Chen , WenLin , Ji and Chen , C. S.}, title = {The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {4}, pages = {477--493}, abstract = {

In this paper, we investigate the method of fundamental solutions (MFS) for solving exterior Helmholtz problems with high wave-number in axisymmetric domains. Since the coefficient matrix in the linear system resulting from the MFS approximation has a block circulant structure, it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space. Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.13-13S04}, url = {http://global-sci.org/intro/article_detail/aamm/81.html} }
TY - JOUR T1 - The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number AU - Chen , Wen AU - Lin , Ji AU - Chen , C. S. JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 477 EP - 493 PY - 2013 DA - 2013/08 SN - 5 DO - http://doi.org/10.4208/aamm.13-13S04 UR - https://global-sci.org/intro/article_detail/aamm/81.html KW - Method of fundamental solutions, exterior Helmholtz problem, circulant matrix, fast Fourier transform, axisymmetric domain. AB -

In this paper, we investigate the method of fundamental solutions (MFS) for solving exterior Helmholtz problems with high wave-number in axisymmetric domains. Since the coefficient matrix in the linear system resulting from the MFS approximation has a block circulant structure, it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space. Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains.

Chen , WenLin , Ji and Chen , C. S.. (2013). The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number. Advances in Applied Mathematics and Mechanics. 5 (4). 477-493. doi:10.4208/aamm.13-13S04
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