Study of the Stability and Accuracy of a Nonconvolutional, Split-Field Perfectly Matched Layer(PML) for Wave Propagation in Elastic Media

Abstract eng:
The Perfectly Matched Layer (PML) model is a material boundary condition for wave propagation in unbounded domains. It consists of an absorbing layer of finite width that surrounds the physical domain of interest so that all outgoing waves are damped out irrespective of their frequency and direction of propagation. The main feature of the PML is that, before discretization it does not generate reflections at the interface separating the PML and the physical medium, however a small reflection is always present after discretization. The satisfactory performance of the PML has resulted in considerable work towards its implementation in several wave-like problems including elastic wave propagation. In the present work we propose and implement a non-convolutional, split-field PML, referred to as the Multi-Axial Perfectly Matched Layer (M-PML). The formulation is obtained by generalizing the ‘classical’ PML to a medium in which damping profiles are specified in more than one direction. Under the hypothesis of small damping and using an eigenvalue sensitivity analysis based on first derivatives, we propose a method to study the stability of the M-PML and demonstrate that it is related to the ratios of the damping profiles. A general procedure for constructing stable M-PML models for elastic media is then obtained. The effectiveness of the M-PML and its advantages relative to the classical PML, are demonstrated by constructing stable terminations for both isotropic as well as anisotropic 2-D media. As a final step in our analysis, we present a quantitative assessment of the accuracy of the proposed M-PML.

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