Mimetic discretization and higher order time integration for acoustic, electromagnetic and elastodynamic wave propagation

Abstract

This paper is devoted to the simulation of acoustic, electromagnetic and elastodynamic wave propagation problems in a unified manner. We focus on the finite integration technique for the spatial discretization of the first-order wave equation systems using lowest order elements. A universal framework of staggered grids is set up in which the application of the finite integration technique for acoustics, electromagnetics and elastodynamics can be combined. This framework offers opportunities to get generic and more efficient implementations. The mimetic properties of the discretization technique are outlined. For the time integration, the use of a class of higher order time integrators with close resemblance to the classical leapfrog method is discussed. It is shown that for the considered wave propagation problems higher order time integrators compare favourably to the classical second leapfrog order scheme, even in combination with a low order spatial discretization.