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A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures

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Listed:
  • Liyuan Lan

    (National Engineering Research Center for Intelligent Electrical Vehicle Power System, College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China)

  • Suifu Cheng

    (National Engineering Research Center for Intelligent Electrical Vehicle Power System, College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China)

  • Xiatao Sun

    (School of Engineering and Applied Science, University of Pennsylvania, Philadelphia, PA 19104, USA)

  • Weiwei Li

    (School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, China)

  • Chao Yang

    (College of Materials Science and Engineering, Qingdao University, Qingdao 266071, China)

  • Fajie Wang

    (National Engineering Research Center for Intelligent Electrical Vehicle Power System, College of Mechanical and Electrical Engineering, Qingdao University, Qingdao 266071, China)

Abstract

This paper proposes a fast meshless scheme for acoustic sensitivity analysis by using the Burton–Miller-type singular boundary method (BM-SBM) and recursive skeletonization factorization (RSF). The Burton–Miller formulation was adopted to circumvent the fictitious frequency that occurs in external acoustic analysis, and then the direct differentiation method was used to obtain the sensitivity of sound pressure to design variables. More importantly, RSF was employed to solve the resultant linear system obtained by the BM-SBM. RSF is a fast direct factorization technique based on multilevel matrix compression, which allows fast factorization and application of the inverse in solving dense matrices. Firstly, the BM-SBM is a boundary-type collocation method that is a straightforward and accurate scheme owing to the use of the fundamental solution. Secondly, the introduction of the fast solver can effectively reduce the requirement of computer memory and increase the calculation scale compared to the conventional BM-SBM. Three numerical examples including two- and three-dimensional geometries indicate the precision and efficiency of the proposed fast numerical technique for acoustic design sensitivity analysis associated with large-scale and complicated structures.

Suggested Citation

  • Liyuan Lan & Suifu Cheng & Xiatao Sun & Weiwei Li & Chao Yang & Fajie Wang, 2022. "A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures," Mathematics, MDPI, vol. 10(20), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3817-:d:943707
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    References listed on IDEAS

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    1. Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
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    Cited by:

    1. Cheng Chi & Fajie Wang & Lin Qiu, 2023. "A Novel Coupled Meshless Model for Simulation of Acoustic Wave Propagation in Infinite Domain Containing Multiple Heterogeneous Media," Mathematics, MDPI, vol. 11(8), pages 1-15, April.

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