A novel time-marching scheme using numerical Green’s functions: A comparative study for the scalar wave equation

The present paper presents the formulation of a novel time-marching method based on the Explicit Green’s Approach (ExGA) to solve scalar wave propagation problems. By means of the weighted residual method in both time and space, the time integral expression concerning the ExGA is readily established. The arising ExGA time integral expression is spatially discretized in a finite element sense and a recursive scheme that employs time-domain numerical Green’s function matrices is adopted to evaluate the displacement and the velocity vectors. These Green’s matrices are computed by the time discontinuous Galerkin finite element method only at the first time step. The system of coupled equations originated from the time discontinuous Galerkin method is then solved by an iterative predictor–multicorrector algorithm. Once the Green’s matrices are computed, no iterative process is required to obtain the displacement and the velocity vectors at any time level. At the end of the paper, numerical examples are presented in order to compare the proposed approach with other approaches.