Three-dimensional solutions of equations of dynamic elasticity by a New Rapid Expansion Method (REM)

This work represents a new scheme for time integration of direct solution methods such as finite-difference, finite-element, and Fourier methods. Forward nodellng with elastic wave propagation is investigated. The rapid expansion method (REM), which we have developed, is based on a modified Chebychev expansion of the formal solution to the governing equations. The REM implementation of the equations of dynamic elasticity using the Fourier method is similar to previous development featuring conventional time integration of second order differencing. A high degree of parallelism exists between the calculations in one time step with temporal differencing and REM calculations. Spatial partial derivatives are computed in the same manner. Compared to time integration of second order differencing, larger time steps or increments are permissible with the REM implementation. For output time sections, results at intermediate times are obtained by resubstituting intermediate times in the computational equations. This does not require recomputation of spatial partial derivatives. The REM can be used to increase accuracy or to obtain comparable accuracy with fewer computations. Conventional time integration and REM methods have been implemented on the CRAY X-MP computer system using parallel processing and the large memory of the Solid-state Storage Device (SSD). The REM can be applied to acoustic and elastic wave propagation using formulations other than the Fourier method.