The novel backward substitution method for the simulation of three-dimensional time-harmonic elastic wave problems

Abstract

This paper presents the newly developed backward substitution method to the simulation of three-dimensional time-harmonic elastic wave problems. This method tries to convert original problem into the one with homogeneous boundary conditions. Then the numerical solution is approximated using modified basis functions with a series of parameters. The solution is assembled by the one obtained from the boundary condition approximation and the one obtained by enforcing the governing equations which are solved separately. This paper firstly extends the backward substitution method to the three-dimensional time harmonic elastic wave problems with three governing equations and its accuracy and convergence is verified through two examples.