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The efficiency of spectral-element and finite-element methods in acoustic wave propagation

Author Affiliations

  • 1Institute of Geophysics, University of Tehran, Tehran, Iran
  • 2Institute of Geophysics, University of Tehran, Tehran, Iran
  • 3Delft University of Technology, Delft, Netherland

Int. Res. J. Earth Sci., Volume 8, Issue (1), Pages 8-12, February,25 (2020)


One of the great technique for surveying of the Earth's subsurface is to simulate seismic wave propagation using numerical modeling. Various numerical approaches are available for simulation of wave propagation in different media, including finite-difference method (FDM), discontinuous Galerkin method (DGM), finite-element method (FEM), finite volume method (FVM), and spectral-element method (SEM). Among different simulation approaches, FEM is a popular method in order to modelling of wave propagation because of flexibility and efficiency for simulation in complex geometries and inhomogeneous media. Standard FEM is an implicit method that means a linear system is required to be solved. Accordingly, it is a slower method that FDM as a result it limited the applicability to seismology. Solving such algorithms on parallel computers with distributed memory complicates matters further. In order to avoid this undesired problem, the spectral-element numerical approach is introduced for simulation of wave propagation. The formulations and equations of SEM is almost as same as that FEM with a tiny differences which makes it more suitable and optimal than finite-element method in the time-domain modelling. In fact, SEM is almost a new numerical technique for simulation of wave propagation. The purpose of this study is proposing the differences between the spectral-element method and finite-element method for simulating seismic wave propagation in different angle with straightforward formulation. The accuracy of the methods are shown by comparing the finite-element and spectral-element solutions with analytical solutions of the two-dimensional (2D) model. Numerical modeling examples show the great performance of the spectral-element scheme over finite-element method.


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