A convolutional dispersion relation preserving scheme for the acoustic wave equation

Abstract

We propose a numerical scheme for approximating the solution of the two dimensional acoustic wave problem. We use machine learning to find a stencil suitable even for high wavenumbers. The proposed scheme incorporates physics informed elements from the field of dispersion-relation-preserving (DRP) schemes into a convolutional optimization machine learning algorithm. We test the proposed method and demonstrate that it performs better than classical and DRP explicit methods for a wide range of wavenumbers.