Finite‐element method for elastic wave propagation

The object of this work is to analyse the computational aspects of the finite‐element method for the elastic wave equations. The necessary numerical techniques are analysed from the point of view of accuracy, performance and storage requirements when implemented in scalar and vector processors with large storage capacity. The method is implemented on an IBM 3090 with vector facility. For this implementation we consider five different time integration schemes (explicit and implicit central difference, Houbolt, constant average acceleration and Wilson), and in the implicit case, both direct (Gaussian decomposition) and iterative (successive over‐relaxation, Jacobi semi‐iterative, Jacobi conjugate gradient) sparse linear systems solvers. These solvers are taken from the ITPACK2C and ESSL libraries using in each case the adequate representation scheme; skyline, row‐wise and compressed diagonal. From our results it is concluded that constant average acceleration and explicit central difference are the most adequate integration methods and Jacobi conjugate gradient is the most efficient solver.