A Poly-Grid Spectral Element Approach for Wave Modeling in Heterogeneous Elastic Solids

Abstract eng:
A wide range of applications requires the modeling of wave propagation phenomena in elastic media with variable physical properties in the domain of interest, while highly accurate algorithms are needed to avoid unphysical effects. Spectral element methods (SEM) have excellent properties of accuracy and flexibility in describing complex models both acoustic and elastic. In the standard SEM approach the element sizes are large compared to the minimum propagating wavelength, so that a single element may handle more than one of the shortest waves. However, computational efficiency is seriously reduced for finely heterogeneous and complex media with property fluctuations shorter than the minimum wavelength; grid resolution down to the finest scales is required, leading to an extremely large problem dimension. The wavelength scale of interest is much larger but cannot be exploited in order to reduce the problem size. As in multiscale problems, the quest is for a method able to solve the macroscopic behavior without solving explicitly the microscopic one. A poly-grid Chebyshev spectral element method (PGCSEM) can overcome this limitation. In order to accurately deal with property variation in the medium, temporary auxiliary grids are introduced which avoid the need of using large meshes, and at the macroscopic level the wave propagation is solved maintaining the SEM accuracy and computational efficiency as confirmed by numerical results. An example is presented in the figure showing an impulse wave propagating against an obstacle with structure details smaller than the size of the elements. We see that a finer mesh, with element boundary following the interface shape of the obstacle, is not needed in order to get the related wavefield propagation.

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