An ACA-BM-SBM for 2D acoustic sensitivity analysis
In this paper, we present a novel computational approach (named ACA-BM-SBM) for the calculation of 2D acoustic sensitivity by combining the Burton-Miller-type singular boundary method (BM-SBM) with the adaptive cross-approximation (ACA) algorithm. The BM-SBM circumvents the source singularities of t...
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| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024096?viewType=HTML |
| _version_ | 1797355287123853312 |
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| author | Liyuan Lan Zhiyuan Zhou Hanqing Liu Xing Wei Fajie Wang |
| author_facet | Liyuan Lan Zhiyuan Zhou Hanqing Liu Xing Wei Fajie Wang |
| author_sort | Liyuan Lan |
| collection | DOAJ |
| description | In this paper, we present a novel computational approach (named ACA-BM-SBM) for the calculation of 2D acoustic sensitivity by combining the Burton-Miller-type singular boundary method (BM-SBM) with the adaptive cross-approximation (ACA) algorithm. The BM-SBM circumvents the source singularities of the fundamental solutions by introducing the origin intensity factors, and it eliminates the fictitious frequency problem in external acoustic fields by introducing the Burton-Miller formula. As a semi-analysis meshless method, the BM-SBM can accurately solve the external acoustic problem governed by the Helmholtz equation. Nevertheless, the computational inefficiency introduced by the dense coefficient matrix renders this method suboptimal, particularly for large-scale simulations. As the number of nodes increases, the computation time and store memory increase dramatically. ACA is a purely algebraic method based on hierarchical matrices which can be used to partition the coefficient matrix step by step. By employing ACA, the BM-SBM can be effectively accelerated, and this results in less computation time, as well as fewer memory requirements. Numerical experiments, including Dirichlet and Neumann boundary conditions, illustrate that the proposed approach is an accurate, efficient and fast numerical method for acoustic sensitivity analysis. |
| first_indexed | 2024-03-08T14:09:54Z |
| format | Article |
| id | doaj.art-6602462d2db9485b8f14eb6f40f1d04b |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T14:09:54Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-6602462d2db9485b8f14eb6f40f1d04b2024-01-15T01:29:49ZengAIMS PressAIMS Mathematics2473-69882024-01-01911939195810.3934/math.2024096An ACA-BM-SBM for 2D acoustic sensitivity analysisLiyuan Lan0Zhiyuan Zhou1Hanqing Liu2Xing Wei3Fajie Wang 41. National Engineering Research Center for Intelligent Electrical Vehicle Power System, College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China2. Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90015, USA1. National Engineering Research Center for Intelligent Electrical Vehicle Power System, College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China3. College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China1. National Engineering Research Center for Intelligent Electrical Vehicle Power System, College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, ChinaIn this paper, we present a novel computational approach (named ACA-BM-SBM) for the calculation of 2D acoustic sensitivity by combining the Burton-Miller-type singular boundary method (BM-SBM) with the adaptive cross-approximation (ACA) algorithm. The BM-SBM circumvents the source singularities of the fundamental solutions by introducing the origin intensity factors, and it eliminates the fictitious frequency problem in external acoustic fields by introducing the Burton-Miller formula. As a semi-analysis meshless method, the BM-SBM can accurately solve the external acoustic problem governed by the Helmholtz equation. Nevertheless, the computational inefficiency introduced by the dense coefficient matrix renders this method suboptimal, particularly for large-scale simulations. As the number of nodes increases, the computation time and store memory increase dramatically. ACA is a purely algebraic method based on hierarchical matrices which can be used to partition the coefficient matrix step by step. By employing ACA, the BM-SBM can be effectively accelerated, and this results in less computation time, as well as fewer memory requirements. Numerical experiments, including Dirichlet and Neumann boundary conditions, illustrate that the proposed approach is an accurate, efficient and fast numerical method for acoustic sensitivity analysis.https://aimspress.com/article/doi/10.3934/math.2024096?viewType=HTMLburton-miller-type singular boundary methodadaptive cross-approximationacoustic sensitivity analysisfast algorithm |
| spellingShingle | Liyuan Lan Zhiyuan Zhou Hanqing Liu Xing Wei Fajie Wang An ACA-BM-SBM for 2D acoustic sensitivity analysis AIMS Mathematics burton-miller-type singular boundary method adaptive cross-approximation acoustic sensitivity analysis fast algorithm |
| title | An ACA-BM-SBM for 2D acoustic sensitivity analysis |
| title_full | An ACA-BM-SBM for 2D acoustic sensitivity analysis |
| title_fullStr | An ACA-BM-SBM for 2D acoustic sensitivity analysis |
| title_full_unstemmed | An ACA-BM-SBM for 2D acoustic sensitivity analysis |
| title_short | An ACA-BM-SBM for 2D acoustic sensitivity analysis |
| title_sort | aca bm sbm for 2d acoustic sensitivity analysis |
| topic | burton-miller-type singular boundary method adaptive cross-approximation acoustic sensitivity analysis fast algorithm |
| url | https://aimspress.com/article/doi/10.3934/math.2024096?viewType=HTML |
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