Application of the FDTD TF/SF method to the analysis of scattering phenomenon of the elastic wave fields in solids

Abstract

The Finite-Difference Time-Domain (FDTD) method is unique in that it can be used to separately calculate the far field scattered waves and near field total waves, a combination of incident plane waves and scattering waves, simultaneously. This formulation, called the total-field/scattered-field (TF/SF) formulation, is very effective for analyzing scattering problems in nondestructive evaluation (NDE). To date, the TF/SF formulation has only been applied to scalar wave fields and electromagnetic wave fields. However, application to the elastic wave fields in solids has not yet been attempted. The present report describes a TF/SF formulation of the elastic wave fields in solids. Specifically, scalar and vector potentials are used for the formulation. Using these potentials is beneficial for two reasons. First, the longitudinal waves and shear waves are initially separated. Therefore, the scattering phenomenon can be clearly recognized. Second, it is simple to use the potentials to set the absorbing boundaries. The FDTD TF/SF formulation has been proven effective for analyzing the scattering phenomenon of a longitudinal plane wave incident to a square hole.