Finite element (FE) studies of energy/material interactions associated with the nondestructive evaluation (NDE) of materials have not only yielded useful information concerning the physics of new NDE phenomena [1] but also provided “test-beds” for the simulation of NDE situations too difficult to replicate in a laboratory environment [2]. FE code has been developed for the analysis of those NDE processes governed by elliptic [3], parabolic [4] and hyperbolic [5] partial differential equation (PDE) types taking advantage of axisymmetry wherever possible in order to conserve computer capacity. In those situations requiring fine spatial and/or temporal discretization, it has been found that the FE code makes excessive demands on even the best computer resources. Examples of this situation include the finite element modeling of the remote field effect in large diameter pipelines [6] and the simulation of ultrasonic wave propagation through large structures [7].