Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media

TLDR

The study presents and analyzes a perfectly matched absorbing layer model for the velocity‑stress formulation of elastodynamics. The method introduces an absorbing layer that decomposes each velocity‑stress component into orthogonal and parallel parts, formulates governing equations for these auxiliary variables, and applies a damping term to the orthogonal component. Experiments demonstrate that the model yields negligible reflection, with a coefficient of about 1 % even for heterogeneous, anisotropic media using only five discretization steps of layer thickness.

Abstract

We present and analyze a perfectly matched, absorbing layer model for the velocity‐stress formulation of elastodynamics. The principal idea of this method consists of introducing an absorbing layer in which we decompose each component of the unknown into two auxiliary components: a component orthogonal to the boundary and a component parallel to it. A system of equations governing these new unknowns then is constructed. A damping term finally is introduced for the component orthogonal to the boundary. This layer model has the property of generating no reflection at the interface between the free medium and the artificial absorbing medium. In practice, both the boundary condition introduced at the outer boundary of the layer and the dispersion resulting from the numerical scheme produce a small reflection which can be controlled even with very thin layers. As we will show with several experiments, this model gives very satisfactory results; namely, the reflection coefficient, even in the case of heterogeneous, anisotropic media, is about 1% for a layer thickness of five space discretization steps.