Analysis of Reflection Powers from a Perfectly Matched Layer for Elastic Waves in the Frequency Domain Finite Element Model

Abstract

A perfectly matched layer (PML) is useful for truncating the computation region of scattering problems in a finite element analysis (FEA). The approximation of the open region with thick layer and discretization of it with finite elements generates reflection waves from PML boundary. However, reflection powers generated by finite element discretization have not been quantified for elastic waves. In this paper, we explain the reflection from PMLs by discretized wave number analysis of elastic plane-wave scattering, and demonstrate that the results of discretized wave number analysis give satisfactory approximations of FEA.

Perfectly Matched Layers for Elastic Waves in Piezoelectric Solids

“…From the differential form, we have derived PMLs for elastic waves in the Cartesian, 14) cylindrical, and spherical coordinates 15) and demonstrated the validity of our PML constants. 14,16) Our derivation revealed that the contravariant components of stress tensors and the particle displacement vectors in the analytic continuation are not transformed into real space. 14) Therefore, the discrepancy in the stiffness constants derived from the two methods, one is based on the differential form 14,16) and the other use analytic continuation, 7) exists.…”

“…14,16) Our derivation revealed that the contravariant components of stress tensors and the particle displacement vectors in the analytic continuation are not transformed into real space. 14) Therefore, the discrepancy in the stiffness constants derived from the two methods, one is based on the differential form 14,16) and the other use analytic continuation, 7) exists.…”