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.

In 1994 B erenger showed how to construct a perfectly matched absorbing layer for the Maxwell system in rectilinear coordinates. This layer absorbs waves of any wavelength and any frequency without re ection and thus can be used to arti cially terminate the domain of scattering calculations. In this paper we show how to derive and implement the B erenger layer in curvilinear coordinates (in two space dimensions). We prove that an in nite layer of this type can be used to solve time harmonic scattering problems. We also show that the truncated B erenger problem has a solution except at a discrete set of exceptional frequencies (which might be empty). Finally numerical results show that the curvilinear layer can produce accurate solutions in the time and frequency domain.

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