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Volume 14, Issue 2
Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics

Junpu Li, Zhuojia Fu, Yan Gu & Qing-Hua Qin

Adv. Appl. Math. Mech., 14 (2022), pp. 315-343.

Published online: 2022-01

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  • Abstract

With the rapid development of computer technology, numerical simulation has become the third scientific research tool besides theoretical analysis and experimental research. As the core of numerical simulation, constructing efficient, accurate and stable numerical methods to simulate complex scientific and engineering problems has become a key issue in computational mechanics. The article outlines the application of singular boundary method to the large-scale and high-frequency acoustic problems. In practical application, the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency sound field. This article focuses on the following two research areas. They are how to discretize partial differential equations into more appropriate linear equations, and how to solve linear equations more efficiently. The bottleneck problems encountered in the computational acoustics are used as the technical routes, i.e., efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies. The article reviews recent advances in emerging applications of the singular boundary method for computational acoustics. This collection can provide a reference for simulating other more complex wave propagation.

  • Keywords

Singular boundary method, origin intensity factor, high-frequency acoustic problems, large-scale acoustic problems, Helmholtz equation.

  • AMS Subject Headings

65N80, 65N35, 65N38, 86-08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-315, author = {Junpu and Li and and 22045 and and Junpu Li and Zhuojia and Fu and and 22046 and and Zhuojia Fu and Yan and Gu and and 22047 and and Yan Gu and Qing-Hua and Qin and and 22048 and and Qing-Hua Qin}, title = {Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {2}, pages = {315--343}, abstract = {

With the rapid development of computer technology, numerical simulation has become the third scientific research tool besides theoretical analysis and experimental research. As the core of numerical simulation, constructing efficient, accurate and stable numerical methods to simulate complex scientific and engineering problems has become a key issue in computational mechanics. The article outlines the application of singular boundary method to the large-scale and high-frequency acoustic problems. In practical application, the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency sound field. This article focuses on the following two research areas. They are how to discretize partial differential equations into more appropriate linear equations, and how to solve linear equations more efficiently. The bottleneck problems encountered in the computational acoustics are used as the technical routes, i.e., efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies. The article reviews recent advances in emerging applications of the singular boundary method for computational acoustics. This collection can provide a reference for simulating other more complex wave propagation.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0356}, url = {http://global-sci.org/intro/article_detail/aamm/20200.html} }
TY - JOUR T1 - Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics AU - Li , Junpu AU - Fu , Zhuojia AU - Gu , Yan AU - Qin , Qing-Hua JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 315 EP - 343 PY - 2022 DA - 2022/01 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0356 UR - https://global-sci.org/intro/article_detail/aamm/20200.html KW - Singular boundary method, origin intensity factor, high-frequency acoustic problems, large-scale acoustic problems, Helmholtz equation. AB -

With the rapid development of computer technology, numerical simulation has become the third scientific research tool besides theoretical analysis and experimental research. As the core of numerical simulation, constructing efficient, accurate and stable numerical methods to simulate complex scientific and engineering problems has become a key issue in computational mechanics. The article outlines the application of singular boundary method to the large-scale and high-frequency acoustic problems. In practical application, the key issue is to construct efficient and accurate numerical methodology to calculate the large-scale and high-frequency sound field. This article focuses on the following two research areas. They are how to discretize partial differential equations into more appropriate linear equations, and how to solve linear equations more efficiently. The bottleneck problems encountered in the computational acoustics are used as the technical routes, i.e., efficient solution of dense linear system composed of ill-conditioned matrix and stable simulation of wave propagation at low sampling frequencies. The article reviews recent advances in emerging applications of the singular boundary method for computational acoustics. This collection can provide a reference for simulating other more complex wave propagation.

Junpu Li, Zhuojia Fu, Yan Gu & Qing-Hua Qin. (2022). Recent Advances and Emerging Applications of the Singular Boundary Method for Large-Scale and High-Frequency Computational Acoustics. Advances in Applied Mathematics and Mechanics. 14 (2). 315-343. doi:10.4208/aamm.OA-2020-0356
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