An explicit time-stepping technique for elastic waves under concepts of Green’s functions computed locally by the FEM

This work presents a new time-marching scheme able to reduce spurious (unphysical) oscillations by means of algorithm damping ratio for elastic wave propagation problems in the framework of the Explicit Green’s Approach (ExGA) (Mansur WJ, et al. J Comp Phys 2007; 227:851–870). The integral expression concerned with the ExGA is written in terms of the Green’s and the Step response functions. Their computations are carried out independently by means of the semidiscrete FEM and the Central difference method. Due to the principle of causality, the Green’s and Step response functions admit a compact support surround the source points for a small enough time step that is usually employed in common explicit time integration methods applied to wave propagation modeling. In this sense, the Green’s and Step response functions at t=Δt can be efficiently computed locally through small subdomains. Each local subdomain with its respective submesh covers only nodes whose Green’s and Step response function values do not vanish. The accuracy and effectiveness of the proposed methodology are demonstrated by analyzing three numerical examples.