Abstract
The propagation of the surface waves in elastic media has been extensively studied and is very important in many fields. The Laplace domain Boundary Element Method (BEM) is powerful and accurate numerical method that can be employed for treating such problems. Since anisotropic elastic problems is very computationally challenging for any BEM formulation, the choice of particular numerical Laplace inversion algorithm is crucial for efficient anisotropic elastodynamic Laplace domain boundary element analysis. In this investigation, for a specific problem of anisotropic linearly elastic half space subjected to transient loading, we examine two different methods for numerical inversion of Laplace transforms. The first method we test is the renowned Durbin’s method which is based on a Fourier series expansion. The second method is the convolution quadrature method which is reformulated as a numerical Laplace transform inversion routine. Methods are compared in the context of their application in the framework of Laplace domain collocation boundary element formulation.
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References
C.Y. Wang, J.D. Achenbach, Elastodynamic fundamental solutions for anisotropic solids. Geophys. J. Int. 118(2), 384 (1994)
C.Y. Wang, J.D. Achenbach, Three-dimensional time-harmonic elastodynamic Green’s functions for anisotropic solids. Proc. R. Soc. A 449(1937), 441 (1995)
F. Durbin, Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate’s method. Comput. J. 17(4), 371 (1974)
K.S. Crump, Numerical inversion of Laplace transforms using a Fourier series approximation. J. ACM 23(1), 89 (1976)
F. de Hoog, J. Knight, A. Stokes, An improved method for numerical inversion of Laplace transforms. SIAM J. Sci. Stat. Comput. 3(3), 357 (1982)
G. Honig, U. Hirdes, A method for the numerical inversion of Laplace transforms. J. Comput. Appl. Math. 10(1), 113 (1984)
X. Zhao, An efficient approach for the numerical inversion of Laplace transform and its application in dynamic fracture analysis of a piezoelectric laminate. Int. J. Solids Struct. 41(13), 3653 (2004)
C. Lubich, Convolution quadrature and discretized operational calculus. I. Numer. Math. 52(2), 129 (1988)
C. Lubich, Convolution quadrature and discretized operational calculus. II. Numer. Math. 52(4), 413 (1988)
M. Schanz, Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach (Springer, Berlin, Heidelberg, 2001), 170p
C.L. Pekeris, The seismic surface pulse. Proc. Natl. Acad. Sci. 41(7), 469 (1955)
M. Eskandari-Ghadi, S. Sattar, Axisymmetric transient waves in transversely isotropic half-space. Soil Dyn. Earthq. Eng. 29(2), 347 (2009)
H.G. Georgiadis, D. Vamvatsikos, I. Vardoulakis, Numerical implementation of the integral-transform solution to Lamb’s point-load problem. Comput. Mech. 24(2), 90 (1999)
J. Xiao, W. Ye, L. Wen, Efficiency improvement of the frequency-domain BEM for rapid transient elastodynamic analysis. Comput. Mech. 52(4), 903 (2013)
M. Schanz, W. Ye, J. Xiao, Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method. Comput. Mech. 57(4), 523 (2016)
P. Wynn, On a device for computing the em(Sn) transformation. Math. Tables Other Aids Comput. 10(54), 91 (1956)
Acknowledgements
The work is financially supported by the Russian Science Foundation under grant No. 18-79-00082.
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Markov, I., Igumnov, L. (2020). Comparison of Two Numerical Inverse Laplace Transform Methods with Application for Problem of Surface Waves Propagation in an Anisotropic Elastic Half-Space. In: Parinov, I., Chang, SH., Long, B. (eds) Advanced Materials. Springer Proceedings in Materials, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-030-45120-2_29
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DOI: https://doi.org/10.1007/978-3-030-45120-2_29
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