A new Fast Multipole formulation for the elastodynamic half-space Green始s tensor
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- 作者：St茅phanie Chaillat ; Marc Bonnet
- 关键词：Fast Multipole method ; Boundary element method ; 3-D elastodynamics ; Half-space problems
- 刊名：Journal of Computational Physics
- 出版年：1 February, 2014
- 年：2014
- 卷：258
- 期：Complete
- 页码：787-808
- 全文大小：574 K
文摘
In this article, a version of the frequency-domain elastodynamic Fast Multipole-Boundary Element Method (FM-BEM) for semi-infinite media, based on the half-space Green始s tensor (and hence avoiding any discretization of the planar traction-free surface), is presented. The half-space Green始s tensor is often used (in non-multipole form until now) for computing elastic wave propagation in the context of soil-structure interaction, with applications to seismology or civil engineering. However, unlike the full-space Green始s tensor, the elastodynamic half-space Green始s tensor cannot be expressed using derivatives of the Helmholtz fundamental solution. As a result, multipole expansions of that tensor cannot be obtained directly from known expansions, and are instead derived here by means of a partial Fourier transform with respect to the spatial coordinates parallel to the free surface. The obtained formulation critically requires an efficient quadrature for the Fourier integral, whose integrand is both singular and oscillatory. Under these conditions, classical Gaussian quadratures would perform poorly, fail or require a large number of points. Instead, a version custom-tailored for the present needs of a methodology proposed by Rokhlin and coauthors, which generates generalized Gaussian quadrature rules for specific types of integrals, has been implemented. The accuracy and efficiency of the proposed formulation is demonstrated through numerical experiments on single-layer elastodynamic potentials involving up to about degrees of freedom. In particular, a complexity significantly lower than that of the non-multipole version is shown to be achieved.