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力学学报  2014 

弹性动力学高阶核无关快速多极边界元法

DOI: 10.6052/0459-1879-13-426, PP. 776-785

Keywords: 弹性动力学,核无关快速多极算法,边界元法,高阶Nystr?,m方法

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Abstract:

基于核无关的快速多极方法,发展了一种弹性动力学问题的快速、高精度边界元分析方法.采用基于二次曲面单元的Nystr?m离散,将边界积分方程转化为求和形式,可以方便地进行加速计算;由于采用二次元,边界元分析精度很高.将一种新型快速多极方法用于Nystr?m边界元法的加速计算,该方法的数值实现简便、不依赖于积分方程基本解的表达式,因此通用性很好;该方法还具有最优的计算量和存储量、精度高且可以控制.结合Nystr?m边界元系数矩阵和快速多极方法转换矩阵的特点,提出一种大幅度降低边界元内存消耗的策略.数值结果表明,该方法无论在分析精度,还是计算速度和内存消耗上,都大大优于同类方法,是一种快速、通用的工程弹性动力学问题大规模数值分析方法.

References

[1]  Gao XW. An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals. Computer Methods in Applied Mechanics and Engineering. 2010, 199: 2856-2864
[2]  Xie GZ, Zhou FL, Zhang JM, et al. New variable transformations for evaluating nearly singular integrals in 3D boundary element method. Engineering Analysis with Boundary Elements. 2013, 37(9): 1169-1178
[3]  张耀明, 谷岩, 陈正宗. 位势边界元法中的边界层效应与薄体结构. 力学学报. 2010, 42(2): 119-227 (Zhang Yaoming, Gu Yan, Chen Jeng-Tzong. Boundary layer effect and thin body structure in BEM for potential problems. Chinese Journal of Theoretical and Applied Mechanics. 2010, 42(2): 119-227 (in Chinese))
[4]  姚振汉, 王海涛. 边界元法. 北京: 高等教育出版社, 2010 (Yao Zhenghan, Wang Haitao. Boundary Element Method. Beijing: Higher Education Press. 2010 (in Chinese))
[5]  Benedetti I, Aliabadi MH, A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems. International Journal for Numerical Methods in Engineering. 2010, 84: 1038-1067
[6]  Chen YC, Hwu C. Boundary element method for vibration analysis of two dimensional anisotropic elastic solids containing holes, cracks or interfaces. Engineering Analysis with Boundary Elements. 2014, 40: 22-35
[7]  Lei J, Felie GS, Zhang CZ. Determination of dynamic intensity factors and time-domain BEM for interfacial cracks in anisotropic piezoelectric materials. International Journal of Solid and Structures. 2013, 50(9): 1482-1493
[8]  Otani Y, Takahashi T, Nishimura N. A fast boundary integral equation method for elastodynamics in time domain and its parallelisation. Boundary Element Analysis, Lecture Notes in Applied and Computational Mechanics . 2007, 29: 161-185
[9]  Fata SN, Cuzina B. A linear sampling method for near field inverse problems in elastodynamics. Inverse Problems. 2004, 20: 713-736
[10]  Greengard L, Rokhlin V. A fast algorithm for particle simulations. Journal of Computational Physics. 1987, 73: 325-348
[11]  李善德, 黄其柏, 李天匀. 新的对角形式快速多极边界元法求解Helmholtz方程. 物理学报. 2012, 61(6): 064301-1-064301-8 (Li Shande, Huang Qibai, Li Tianyun. A new diagonal form fast multipole boundary element method for solving acoustic Helmholtz equation. Acta Physica Sinica. 2012, 61(6): 064301-1-064301-8 (in Chinese))
[12]  Phillips JR, White JK. A procorrected-FFT method for electrostatic analysis of complicated 3-D structures. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 1997, 16(10) 1059-1072
[13]  Bebendorf M. Hierarchical matrices: A means to efficiently solve elliptic boundary value problems Vol.63. In: Lecture Notes in Computational Science and Engineering (LNCSE). Springer-Verlag, 2008. ISBN 978-3-540-77146-3
[14]  Xiao JY, Wen LH, Tausch J. On fast matrix-vector multiplication in wavelet Galerkin BEM. Engineering Analysis with Boundary Elements. 2009, 33(2): 159-167
[15]  Chaillat S, Bonnet M, Semblat JF. A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain. Computer Methods in Applied Mechanics and Engineering. 2008, 197 4233-4249
[16]  Chaillat S, Semblat JF, Bonnet M. A preconditioned 3-D multi-region fast multipole solver for seismic wave propagation in complex geometries. Communications in Computational Physics. 2012, 11(2): 594-609
[17]  Milazzo A, Benedetti L, Aliabadi MH. Hierarchical fast BEM for anisotropic time-harmonic 3-D elastodynamics. Computers and Structures. 2012, 97: 9-24
[18]  Yan ZY, Zhang J, Ye WJ. Rapid solution of 3-D oscillatory elastodynamics using the pFFT accelerated BEM. Engineering Analysis with Boundary Elements. 2010, 34(11): 956-962
[19]  Xiao JY, Ye WJ, Cai YX, et al. Precorrected FFT accelerated BEM for large-scale transient elastodynamic analysis using frequency-domain approach. International Journal for Numerical Methods in Engineering. 2011, 90(1): 116-134
[20]  Xiao JY, Ye WJ, Wen LH. Efficiency improvement of the frequency-domain BEM for rapid transient elastodynamic analysis. Computational Mechanics, 2013, 52(4): 903-912
[21]  Ying LX, Biros G, Zorin D. Kernel-independent adaptive fast multipole algorithm in two and three dimensions. Journal of Computational Physics. 2004, 196: 591-626
[22]  Fong W, Darve E. The black-box fast multipole method. Journal of Computational Physics. 2009, 228: 8712-8725.
[23]  Engquist B, Ying LX. Fast directional multilevel algorithms for oscillatory kernels. SIAM Journal of Scientific Computation. 2007, 29(4): 1710-1737.
[24]  Messner M, Schanz M, Darve E. Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation. Journal of Computational Physics. 2012, 231(4): 1175-1196
[25]  Liu YJ, Li YX. Slow convergence of the BEM with constant elements in solving beam bending problems. Engineering Analysis with Boundary Elements. 2014, 39: 1-4
[26]  Gao XW, Davies TG. Boundary Element Programming in Mechanics. Cambridge University Press (ISBN: 052177359-8), 2002
[27]  Canino LF, Ottusch JJ, Stalzer MA, et al. Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nystr?m discretization. Journal of Computational Physics. 1998, 146: 627-663
[28]  Bremer J, Gimbutas Z. A Nystr?m method for weakly singular integral operators on surfaces. Journal of Computational Physics. 2012, 231: 4885-4903
[29]  Mei ST, Chew WC. Nystr?m method for elastic wave scattering by three-dimensional obstacles. Journal of Computational Physics. 2007, 226: 1845-1858
[30]  Mei ST, Chew WC. Multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects. Journal of Computational Physics. 2009, 228: 921-932
[31]  Rong JJ, Wen LH, Xiao JY. Efficiency improvement of the polar coordinate transformation for evaluating BEM singular integrals on curved elements. Engineering Analysis with Boundary Elements. 2014, 38: 83-93

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