Abstract
In this work we consider the numerical solution of elastic wave propagation problems in heterogeneous media. Our approximation is based on a Discontinuous Galerkin spectral element method coupled with a fourth stage Runge-Kutta time integration scheme. We partition the computational domain into non-overlapping subregions, according to the involved materials, and in each subdomain a spectral finite element discretization is employed. The partitions do not need to be geometrically conforming; furthermore, different polynomial approximation degrees are allowed within each subdomain. The numerical results show that the proposed method is accurate, flexible and well suited for wave propagation analysis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Antonietti, P.F., Mazzieri, I., Quarteroni, A., Rapetti, F.: Non-conforming high order approximations of the elastodynamics equation. Comput. Meth. Appl. Mech. Eng. 209–212, 212–238 (2012)
Chaljub, E., Capdeville, Y., Vilotte, J.P.: Solving elastodynamics in a fluid-solid heterogeneous sphere: a parallel spectral element approximation on non-conforming grids. J. Comput. Phys. 187(2), 457–491 (2003)
Clayton, R., Engquist, B.: Absorbing boundary conditions for acoustic and elastic wave equations, Bull. Seism. Soc. Am. 67, 1529–1540 (1977)
Cohen, G.C.: Higher-order numerical methods for transient wave equations. Springer-Verlag, Berlin (2002)
Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral methods - Fundamentals in single domains, Springer-Verlag, Berlin, (2006)
Faccioli, E., Maggio, F., Paolucci, R., Quarteroni, A.: 2-D and 3-D elastic wave propagation by a pseudo-spectral domain decomposition method. J. of Seismol. 1, 237–251 (1997)
Givoli, D.: Non-reflecting boundary conditions: review article. J. Comput. Phys. 94, 1–29 (1991)
Grote, M.J., Schneebeli, A., Schotzau, D.: Discontinuous Galerkin finite element method for the wave equation. SIAM J. Numer. Anal. 44(6), 2408–2431 (2006)
de la Puente, J., Kaser, M., Dumbser, M., Igel, H.: An arbitrary high-order discontinuous Galerkin method for elastic waves on unstructured meshes – IV. Anisotropy. Geophys. J. Int. 169(3), 1210–1228 (2007)
Komatitsch, D., Tromp, J.: Introduction to the spectral-element method for 3-D seismic wave propagation. Geophys. J. Int. 139, 806–822 (1999)
Lambert, J.D.: Numerical methods for ordinary differential systems: the initial value problem. John Wiley & Sons Inc., New York, USA (1991)
Mercerat, E.D., Vilotte, J.P., Sanchez-Sesma, F.J.: Triangular spectral-element simulation of two-dimensional elastic wave propagation using unstructured triangular grids. Geophys. J. Int. 166(2), 679–698 (2006)
Mazzieri, I.: Non-conforming high order methods for the elastodynamics equation. PhD. Thesis, Politecnico di Milano (2012)
Mazzieri, I., Smerzini, C., Antonietti, P.F., Rapetti, F., Stupazzini, M., Paolucci, R., Quarteroni, A.: Non-conforming spectral approximations for the elastic wave equation in heterogeneous media, Proceedings of COMPDYN 2011, 3rd International Conference in Computational Methods in Structural Dynamics and Earthquake Engineering (2011)
Priolo, E., Carcione, J.M., Seriani, G.: Numerical simulation of interface waves by high-order spectral modeling techniques. J. Acoust. Soc. Am. 95(2), 681–693 (1994)
Stacey, R.: Improved transparent boundary formulations for the elastic-wave equation. Bull. Seismol. Soc. Am. 78(6), 2089–2097 (1988)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Antonietti, P.F., Mazzieri, I., Quarteroni, A., Rapetti, F. (2014). High Order Space-Time Discretization for Elastic Wave Propagation Problems. In: Azaïez, M., El Fekih, H., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012. Lecture Notes in Computational Science and Engineering, vol 95. Springer, Cham. https://doi.org/10.1007/978-3-319-01601-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-01601-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01600-9
Online ISBN: 978-3-319-01601-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)