An ACA-BM-SBM for 2D acoustic sensitivity analysis

Liyuan Lan; Zhiyuan Zhou; Hanqing Liu; Xing Wei; Fajie Wang; Liyuan Lan; Zhiyuan Zhou; Hanqing Liu; Xing Wei; Fajie Wang

doi:10.3934/math.2024096

AIMS Mathematics

2024, Volume 9, Issue 1: 1939-1958. doi: 10.3934/math.2024096

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Research article

An ACA-BM-SBM for 2D acoustic sensitivity analysis

1.
National Engineering Research Center for Intelligent Electrical Vehicle Power System, College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China
2.
Viterbi School of Engineering, University of Southern California, Los Angeles, CA 90015, USA
3.
College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang 330013, China

Received: 24 September 2023 Revised: 22 November 2023 Accepted: 04 December 2023 Published: 18 December 2023
MSC : 65N35, 68W99, 76M99

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.
- Burton-Miller-type singular boundary method,
- adaptive cross-approximation,
- acoustic sensitivity analysis,
- fast algorithm
Citation: Liyuan Lan, Zhiyuan Zhou, Hanqing Liu, Xing Wei, Fajie Wang. An ACA-BM-SBM for 2D acoustic sensitivity analysis[J]. AIMS Mathematics, 2024, 9(1): 1939-1958. doi: 10.3934/math.2024096

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Abstract

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.

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