Modelling of Scalar Wave Propagation Problems in Heterogeneous Media by the Explicit Green's Approach Method

Abstract

The Explicit Green's approach is an effective method for solving initial-boundary value problems in any kind of medium and geometry. This is due to the fact that numerical Green's functions are adopted instead of analytical ones, rendering a more general approach. When the Explicit Green's approach is applied to the scalar wave equation and Green's functions are computed by the finite element method (FEM) in conjunction with the central difference time integration scheme, unstable results are observed. To circumvent this drawback, the present paper discusses the application of a time substep procedure to the central difference time integration for the Green's functions computation. The substep procedure has the advantage of stabilizing the solution as well as increasing the accuracy order in the time domain from two to four. Numerical examples that demonstrate the accuracy and effectiveness of the proposed methodology are provided.