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A Mixed Perfectly-Matched-Layer for Transient Wave Simulations in Axisymmetric Elastic Media

S. Kucukcoban1, L.F. Kallivokas2
Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, 1 University Station, C1748, TX 78712, USA
Department of Civil, Architectural and Environmental Engineering, The University of Texas at Austin, 1 University Station, C1748, TX 78712, USA

Computer Modeling in Engineering & Sciences 2010, 64(2), 109-146. https://doi.org/10.3970/cmes.2010.064.109

Abstract

We are concerned with elastic wave simulations arising in elastic, semi-infinite, heterogeneous, three-dimensional media with a vertical axis of symmetry through the coordinate origin. Specifically, we discuss the development of a new mixed displacement-stress formulation in PML-truncated axisymmetric media for forward elastic wave simulations. Typically, a perfectly-matched-layer (PML) is used to surround a truncated finite computational domain in order to attenuate outwardly propagating waves without reflections for all non-zero angles-of-incidence and frequencies. To date, standard formulations use split fields, where the displacement components are split into normal and parallel to the PML interface components. In this work, we favor unsplit schemes, primarily for the computational savings they afford when compared against split-field methods. We use complex-coordinate stretching in the frequency-domain, but retain both unsplit displacements and stresses as unknowns prior to inverting the stretched forms back into the time-domain. We use a non-classical mixed finite element approach, and an extended Newmark-bscheme to integrate in time the resulting semi-discrete forms, which in addition to the standard terms, include a jerk or jolt term. We report on numerical simulations demonstrating the stability and efficacy of the approach.

Keywords

Perfectly matched layer, transient elastodynamics, wave propagation, mixed finite elements, axisymmetric media

Cite This Article

Kucukcoban, S., Kallivokas, L. (2010). A Mixed Perfectly-Matched-Layer for Transient Wave Simulations in Axisymmetric Elastic Media. CMES-Computer Modeling in Engineering & Sciences, 64(2), 109–146.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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