Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation
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APPLIED MATHEMATICS AND MECHANICS (ENGLISH EDITION) https://doi.org/10.1007/s10483-020-2674-6
Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation∗ Linchong CHEN1 , Xiaolin LI2,† 1. School of Mathematics and Information Engineering, Chongqing University of Education, Chongqing 400065, China; 2. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China; (Received Feb. 26, 2020 / Revised Jul. 30, 2020)
Abstract The Burton-Miller boundary integral formulation is solved by a complex variable boundary element-free method (CVBEFM) for the boundary-only meshless analysis of acoustic problems with arbitrary wavenumbers. To regularize both strongly singular and hypersingular integrals and to avoid the computation of the solid angle and its normal derivative, a weakly singular Burton-Miller formulation is derived by considering the normal derivative of the solid angle and adopting the singularity subtraction procedures. To facilitate the implementation of the CVBEFM and the approximation of gradients of the boundary variables, a stabilized complex variable moving least-square approximation is selected in the meshless discretization procedure. The results show the accuracy and efficiency of the present CVBEFM and reveal that the method can produce satisfactory results for all wavenumbers, even for extremely large wavenumbers such as k = 10 000. Key words meshless method, complex variable moving least-square approximation, boundary element-free method, Burton-Miller formulation, regularization, high frequency acoustic problem, large wavenumber Chinese Library Classification O241.8 2010 Mathematics Subject Classification
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65N38
Introduction
The numerical analysis of acoustic problems has various applications in many scientific fields[1] . In recent years, various meshless methods, such as the singular meshless method[2] , the boundary point interpolation method[3] , the singular boundary method[4] , the localized method of fundamental solutions[5] , the localized boundary knot method[6] , the local radial ∗ Citation: CHEN, L. C. and LI, X. L. Meshless acoustic analysis using a weakly singular BurtonMiller boundary integral formulation. Applied Mathematics and Mechanics (English Edition) (2020) https://doi.org/10.1007/s10483-020-2674-6 † Corresponding author, E-mail: [email protected] Project supported by the National Natural Science Foundation of China (No. 11971085), the Innovation Research Group Project in Universities of Chongqing of China (No. CXQT19018), the Science and Technology Research Program of Chongqing Municipal Education Commission of China (No. KJZD-M201800501), and the Science and Technology Research Program of Chongqing University of Education of China (No. KY201927C) c
The Author(s) 2020
2
Linchong CHEN and Xiaolin LI
point interpolation method[7] , the Galerkin meshfree method[8] , and the element-free Galerkin method[9] , have been applied to acoustic problems. Boundary integral equations (BIEs)[1,10] are powerful and popular for
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