NUMERICAL APPROXIMATION OF ELASTIC-WAVES EQUATIONS BY IMPLICIT SPECTRAL METHODS

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