Abstract
The use of both elastic variables and velocity potentials is proposed for the analysis of elastic wave fields in isotropic solids by finite-difference time-domain (FDTD) methods. The term `elastic variables' refers to stresses and particle velocities. Velocity potentials can be directly derived using the same leap-frog finite-difference scheme as in the FDTD method. In some situations, for example, where an absorbing boundary is present, it is more straightforward to calculate using velocity potentials. This approach also provides an easy way to handle of complex elastic wave phenomena. On the other hand, many other types of boundary conditions are often expressed in terms of elastic variables. In these situations, it is more convenient to use elastic variables for calculation. Some examples are introduced here to illustrate the efficiency of the proposed technique. First, the method was used for the case of an absorbing boundary. In the model, almost all analysis was carried out using values of stress and particle velocity, but velocity potentials were applied near the absorbing boundary on the truncated interface. Second, an interface between elastic variables and velocity potentials, namely a stress-velocity/potentials interface, was constructed around a scattering object. External to the interface, stresses and particle velocities were used for calculation, and potential variables were applied inside the interface. In a third example, calculations were made over almost the entire analytical region using potential values, but in the neighborhood of the free boundary, elastic variables were used. All the examples above were analyzed numerically using the FDTD method, and the results confirmed the usefulness of the method.