A Well-Posed and Discretely Stable Perfectly Matched Layer for Elastic Wave Equations in Second Order Formulation (Communications in Computational Physics, 2012)
We present a well-posed and discretely stable perfectly matched layer forthe anisotropic (and isotropic) elastic wave equations without first re-writing the governing equations as a first order system. The new model is derived by the complexcoordinate stretching technique. Using standard perturbation methods we show thatcomplex frequency shift together with a chosen real scaling factor ensures the decay ofeigen-modes for all relevant frequencies. To buttress the stability properties and the robustness of the proposed model, numerical experiments are presented for anisotropicelastic wave equations. The model is approximated with a stable node-centered finitedifference scheme that is second order accurate both in time and space.