Abstract
To reduce computational complexity and memory requirement for 3-D elastodynamics using the boundary element method (BEM), a multi-level fast multipole BEM (FM-BEM) based on the diagonal form for the expansion of the elastodynamic fundamental solution is proposed and demonstrated on numerical examples involving single-region and multi-region configurations where the scattering of seismic waves by a topographical irregularity or a sediment-filled basin is examined.
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References
Beskos, D. Boundary element methods in dynamic analysis. Appl. Mech. Rev., 40:1–23 (1987).
Beskos, D. Boundary element methods in dynamic analysis, Part. II. Appl. Mech. Rev., 50:149–197 (1997).
Bonnet, M. Boundary Integral Equation Method for Solids and Fluids. Wiley, New York (1999).
Chaillat, S., Bonnet, M., Semblat, J. F. A multi-level fast multipole BEM for 3-D elastodynamics in the frequency domain. Comp. Meth. Appl. Mech. Eng., 197: 4233–4249 (2008).
Chaillat, S., Bonnet, M., Semblat, J. F. A new fast multi-domain BEM to model seismic wave propagation and amplification in 3D geological structures. Geophys. J. Int., in press (2009).
Dangla, P., Semblat, J. F., Xiao, H., Delépine, N. A simple and efficient regularization method for 3D BEM: application to frequency-domain elastodynamics. Bull. Seism. Soc. Am., 95: 1916–1927 (2005).
Darve, E. The fast multipole method : numerical implementation. J. Comp. Phys., 160:195–240 (2000).
Epton, M. A., Dembart, B. Multipole translation theory for the three-dimensional Laplace and Helmholtz equations. SIAM J. Sci. Comp., 16:865–897 (1995).
Eringen, A. C., Suhubi, E. S. Elastodynamics, vol. II-linear theory. Academic Press, New York (1975).
Eshraghi, H., Dravinski, M. Scattering of plane harmonic SH, SV, P and Rayleigh waves by non-axisymmetric three-dimensional canyons: a wave function expansion approach. Earthquake Eng. Struct. Dyn., 18:983–998 (1989).
Fujiwara, H. The fast multipole method for solving integral equations of three-dimensional topography and basin problems. Geophys. J. Int., 140:198–210 (2000).
Gumerov, N. A., Duraiswami, R. Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. Elsevier, Amsterdam (2005).
Guzina, B. B., Pak, R. Y. S. On the analysis of wave motions in a multi-layered solid. Quart. J. Mech. Appl. Math., 54:13–37 (2001).
Mantic, V. A new formula for the C-matrix in the somigliana identity. J. Elast., 33:191–201 (1993).
Mossessian, T. K., Dravinski, M. Amplification of elastic waves by a three dimensional valley. Part 1: steady state response. Earthquake Eng. Struct. Dyn., 19:667–680 (1990).
Nishimura, N. Fast multipole accelerated boundary integral equation methods. Appl. Mech. Rev., 55(4) (2002).
Reinoso, E., Wrobel, L. C., Power, H. Three-dimensional scattering of seismic waves from topographical structures. Soil. Dyn. Earthquake Eng., 16:41–61 (1997).
Rokhlin, V. Diagonal forms of translation operators for the Helmholtz equation in three dimensions. Appl. Comp. Harmonic Anal., 1:82–93 (1993).
Saad, Y., Schultz, M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7:856–869 (1986).
Sánchez-Sesma, F. J. Diffraction of elastic waves by 3D surface irregularities. Bull. Seism. Soc. Am., 73:1621–1636 (1983).
Sylvand, G. La méthode multipôle rapide en éléctromagnétisme : performances, parallélisation, applications. Ph.D. thesis, ENPC, Paris, France (2002).
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Bonnet, M., Chaillat, S., Semblat, JF. (2009). Multi-Level Fast Multipole BEM for 3-D Elastodynamics. In: Manolis, G.D., Polyzos, D. (eds) Recent Advances in Boundary Element Methods. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9710-2_2
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DOI: https://doi.org/10.1007/978-1-4020-9710-2_2
Publisher Name: Springer, Dordrecht
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