A DUAL-LEVEL SINGULAR BOUNDARY METHOD FOR LARGE-SCALE HIGH FREQUENCY SOUND FIELD ANALYSIS
LiJunpu*,, ChenWen*, State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering & Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing 211100, China 中图分类号:O302 文献标识码:A
关键词:奇异边界法;高频声场计算;改进双层算法;无网格方法;源点强度因子 Abstract Numerical simulation of the large-scale high frequency sound field is a computational challenging task. To solve the difficulty that the traditional boundary collocation methods are not easy to be applied to large-scale problems thanks to the resulting large-scale fully-populated matrix, a dual-level singular boundary method is proposed in this study. By introducing a dual level structure, the fully-populated matrix is transformed to a large-scale locally supported sparse matrix on fine mesh. The bottleneck of excessive storage requirements and a large number of operations encountered by the traditional singular boundary method is hereby avoided. Secondly, the method uses only coarse mesh nodes to evaluate far-field contributions, and it is a kernel-independent algorithm. In comparison with the fast multipole method, the dual-level singular boundary method performs higher adaptability and flexibility. In addition, the dual level structure plays a role of preconditioner, which makes the method is very efficient for solving matrix with large scale, high rank and high condition number. In scattering sphere example, the dual-level singular boundary method simulates well the acoustic scattering problem with up to dimensionless wavenumber of 160 when the number of degrees of freedom is taken as 100 000. In the benchmark human head sound scattering, the dual-level singular boundary method using 80 000 degrees of freedom performs 78.13% faster than the COMSOL, and it is noted that the computational frequency is up to 25 kHz, which is far beyond the limit of hearing of human ear.
式(A9)与式(A10)即为赫姆霍兹方程源点强度因子公式. 本附录所推导源点强度因子公式程序均可在奇异工具箱V2.0中找到, 下载网址: https://doi.org/10.13140/RG.2.2.13247.00162. The authors have declared that no competing interests exist.
(LiuJingze, JiangDong, HanXiaolin, et al.Free vibration analysis of curvilinearly stiffened Kirchhoff-Mindlin plates .Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(4): 929-939 (in Chinese)) [本文引用: 1]
[2]
WangXM, LiuS, LiuZP.Underwater sonar image detection: A combination of non-local spatial information and quantum-inspired shuffled frog leaping algorithm .Plos One, 2017, 12(5): 1-30 [本文引用: 1]
[3]
LiJP, ChenW.Singular boundary method based on time-dependent fundamental solutions for active noise control .Numerical Methods for Partial Differential Equations, 2018, 34(4): 1401-1421 [本文引用: 2]
(LiuShuo, FangGuodong, WangBing, et al.Study of thermal conduction problem Using coupled peridynamics and finite element method .Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 339-348 (in Chinese)) [本文引用: 1]
[5]
ZhangJM, LinWC, DongYQ, et al.A double-layer interpolation method for implementation of BEM analysis of problems in potential theory .Applied Mathematical Modelling, 2017, 51: 250-269 [本文引用: 1]
[6]
LiXL, LiSL.Improved complex variable moving least squares approximation for three-dimensional problems using boundary integral equations .Engineering Analysis with Boundary Elements, 2017, 84: 25-34
(GaoXiaowei, LiuJian, PengHaifeng.Integrated unit bem and its application in analysis of actively cooling tps .Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(4): 994-1003 (in Chinese))
[8]
GaoXW, LiZY, YangKai, et al.Element differential method and its application in thermal-mechanical problems .International Journal for Numerical Methods in Engineering, 2018, 113(1): 82-108 [本文引用: 1]
[9]
LiXL, LiSL.Analysis of the complex moving least squares approximation and the associated element-free Galerkin method .Applied Mathematical Modelling, 2017, 47: 45-62
[10]
LiJP, ChenW.A modified singular boundary method for three-dimensional high frequency acoustic wave problems .Applied Mathematical Modelling, 2018, 54: 189-201 [本文引用: 1]
[11]
LiJP, ChenW, GuY.Error bounds of singular boundary method for potential problems .Numerical Methods for Partial Differential Equations, 2017, 33(6): 1987-2004 [本文引用: 1]
(YangJianjun, ZhengJianlong.Meshless local strong-weak (MLSW) method for irregular domain problems .Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 659-666 (in Chinese)) [本文引用: 1]
[13]
ShenL, LiuYJ.An adaptive fast multipole boundary element method for three-dimensional acoustic wave problems based on the Burton-Miller formulation .Computational Mechanics, 2007, 40(3): 461-472 [本文引用: 1]
CuiTJ, WengCC, ChenG, et al.Efficient MLFMA, RPFMA, and FAFFA algorithms for EM scattering by very large structures .IEEE Transactions on Antennas & Propagation, 2004, 52(3): 759-770 [本文引用: 1]
[16]
LiJP, ChenW, Fu ZJ. A modified dual-level algorithm for large-scale three-dimensional Laplace and Helmholtz equation . Computational Mechanics, 2018, https://doi.org/10.1007/s00466-018-1536-2 [本文引用: 4]
(ChenWen, LiJunpu, Fu ZhuoJia. Singular boundary method based on time-dependent fundamental solution for 2D scalar wave equation .Chinese Journal of Computational Mechanics, 2017, 34(2): 231-237 (in Chinese)) [本文引用: 2]
[18]
FuZJ, ChenW, GuY.Burton-Miller-type singular boundary method for acoustic radiation and scattering .Journal of Sound & Vibration, 2014, 333(16): 3776-3793 [本文引用: 1]
[19]
MccowenA.Efficient 3-D moment-method analysis for reflector antennas using a far-field approximation technique .IEE Proceedings-Microwaves, Antennas and Propagation, 1999, 146(1): 7-12 [本文引用: 1]
[20]
ChenJT, LeeYT, LinYJ.Analysis of mutiple-shepers radiation and scattering problems by using a null-field integral equation approach .Applied Acoustics, 2010, 71(8): 690-700 [本文引用: 1]
[21]
LiuL.Single layer regularized meshless method for three dimensional exterior acoustic problem .Engineering Analysis with Boundary Elements, 2017, 77: 138-144 [本文引用: 2]
(GuYan, ChenWen.Improved singular boundary method for three dimensional potential problems .Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(2): 351-360 (in Chinese)) [本文引用: 1]
[23]
LiuL, ZhangH.Single layer regularized meshless method for three dimensional Laplace problem .Engineering Analysis with Boundary Elements, 2016, 71: 164-168 [本文引用: 1]
(WangJunpeng, XiaoJinyou, WenLihua.An efficient numerical method for large-scale modal analysis using boundary element method .Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(5): 1070-1080 (in Chinese)) [本文引用: 1]
[25]
LiJP, FuZJ, ChenW.Numerical investigation on the obliquely incident water wave passing through the submerged breakwater by singular boundary method .Computers & Mathematics with Applications, 2016, 71(1): 381-390 [本文引用: 1]