Numerical approximation of elastic waves equations by implicit spectral methods Original Research Article

A numerical treatment of the linear elasto-dynamic problem is presented. The spatial discretization is based on Legendre collocation methods (also called pseudo-spectral methods) set in weak form, whereas we use implicit integration schemes based on finite differences for the temporal discretization. Absorbing boundary conditions are introduced in order to face wave propagation problems in unbounded domains. We present several numerical results concerning stability, convergence, absorption properties for waves leaving the boundaries, and comparison between explicit and implicit time advancing schemes. The main result of the paper is as follows: the implicit advancing time scheme allows us to adopt an integration step time about ten times larger than the one obtained by assuming an explicit advancing time scheme.