A fast volume integral equation method for elastic wave propagation in a half space
A fast volume integral equation method for elastic wave propagation in a half space
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DOI：
10.1016/j.ijsolstr.2011.07.013
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发表时间：
2011-11
影响因子：
3.6
通讯作者：
T. Touhei
中科院分区：
文献类型：
--
作者：
T. Touhei
开发了一种快速求解体积积分方程的方法，用于半空间中弹性波传播的散射分析。该方法将本研究中提出的快速广义傅立叶变换和逆变换应用于克雷洛夫子空间方法。该方法所需的计算量为 O(NlogN)，其中 N 是用于对弹性半空间建模的网格点的数量。此外，提出了广义傅里叶变换的MPI并行算法，以进一步减少CPU时间。进行数值计算是为了检查采样网格点的数量及其间隔对体积积分方程的解以及分析所需的CPU时间的影响。此外，还对所提出的方法与之前基于梯形方法的方法（Touhei，2009）进行了比较，以讨论本方法解的性质。
A fast method for solving the volume integral equation is developed for scattering analysis of elastic wave propagation in a half space. The proposed method applies the fast generalized Fourier transform and inverse transform formulated in the present study to the Krylov subspace method. The amount of calculations required for the proposed method is O(NlogN), where N is the number of grid points used to model the elastic half space. Furthermore, the MPI parallel algorithm for the generalized Fourier transform is presented for further reduction of the CPU time. Numerical calculations are performed in order to examine the effects of the number of sampling grid points as well as their intervals on the solutions of the volume integral equation and the CPU time required for the analysis. In addition, comparisons of the proposed method with the previous method based on the trapezoidal approach (Touhei, 2009) are also performed in order to discuss the properties of the solution of the present method.