Application of the finite-difference time-domain method and total-field/scattered field formulation to scattering phenomena in solids

Abstract

The finite-difference time-domain (FDTD) numerical method has the unique characteristic that it can separately calculate the far-field scattered waves and near-field total waves at the same time, where total waves refer to a mixture of incident plane waves and scattered waves. This formulation is called the total-field/scattered-field (TF/SF) formulation and is very effective for the analysis of scattering problems in nondestructive evaluation (NDE). In this report, a TF/SF formulation of the elastic wave fields in solids is described. 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 facile to use the potentials for setting the absorbing boundaries. The FDTD TF/SF formulation using potentials has been proved effective in the analysis of the scattering of a longitudinal plane wave incident to a square hole.

An FDTD scheme on a face-centered-cubic (FCC) grid for the solution of the wave equation

“…The FDTD methodology has not been restricted to Maxwell's equations, but has also been utilized in the areas of seismic/acoustic simulations e.g. [2,3], as well as for the computation of elastic waves [4,5].…”