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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

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 = {Wen and Chen and and 20099 and and Wen Chen and Ji and Lin and and 20100 and and Ji Lin and C. S. and Chen and and 20101 and and C. S. Chen}, 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.

Wen Chen, Ji Lin & C. S. Chen. (1970). 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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