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Volume 15, Issue 1
Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material

Zengtao Chen & Fajie Wang

Adv. Appl. Math. Mech., 15 (2023), pp. 182-201.

Published online: 2022-10

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  • Abstract

This paper documents the first attempt to apply a localized method of fundamental solutions (LMFS) to the acoustic analysis of car cavity containing sound-absorbing materials. The LMFS is a recently developed meshless approach with the merits of being mathematically simple, numerically accurate, and requiring less computer time and storage. Compared with the traditional method of fundamental solutions (MFS) with a full interpolation matrix, the LMFS can obtain a sparse banded linear algebraic system, and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains. In the LMFS, only circular or spherical fictitious boundary is involved. Based on these advantages, the method can be regarded as a competitive alternative to the standard method, especially for high-dimensional and large-scale problems. Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.

  • AMS Subject Headings

65N80, 62P30, 35J05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-182, author = {Chen , Zengtao and Wang , Fajie}, title = {Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {15}, number = {1}, pages = {182--201}, abstract = {

This paper documents the first attempt to apply a localized method of fundamental solutions (LMFS) to the acoustic analysis of car cavity containing sound-absorbing materials. The LMFS is a recently developed meshless approach with the merits of being mathematically simple, numerically accurate, and requiring less computer time and storage. Compared with the traditional method of fundamental solutions (MFS) with a full interpolation matrix, the LMFS can obtain a sparse banded linear algebraic system, and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains. In the LMFS, only circular or spherical fictitious boundary is involved. Based on these advantages, the method can be regarded as a competitive alternative to the standard method, especially for high-dimensional and large-scale problems. Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0197}, url = {http://global-sci.org/intro/article_detail/aamm/21131.html} }
TY - JOUR T1 - Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material AU - Chen , Zengtao AU - Wang , Fajie JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 182 EP - 201 PY - 2022 DA - 2022/10 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0197 UR - https://global-sci.org/intro/article_detail/aamm/21131.html KW - Acoustic analysis, localized method of fundamental solutions, car cavity, sound-absorbing material. AB -

This paper documents the first attempt to apply a localized method of fundamental solutions (LMFS) to the acoustic analysis of car cavity containing sound-absorbing materials. The LMFS is a recently developed meshless approach with the merits of being mathematically simple, numerically accurate, and requiring less computer time and storage. Compared with the traditional method of fundamental solutions (MFS) with a full interpolation matrix, the LMFS can obtain a sparse banded linear algebraic system, and can circumvent the perplexing issue of fictitious boundary encountered in the MFS for complex solution domains. In the LMFS, only circular or spherical fictitious boundary is involved. Based on these advantages, the method can be regarded as a competitive alternative to the standard method, especially for high-dimensional and large-scale problems. Three benchmark numerical examples are provided to verify the effectiveness and performance of the present method for the solution of car cavity acoustic problems with impedance conditions.

Zengtao Chen & Fajie Wang. (2022). Localized Method of Fundamental Solutions for Acoustic Analysis Inside a Car Cavity with Sound-Absorbing Material. Advances in Applied Mathematics and Mechanics. 15 (1). 182-201. doi:10.4208/aamm.OA-2021-0197
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