Building Abstractions for Advanced Timestepping in Devito

Historically, wave propagators used for seismic imaging primarily employ the lowest or next-to-lowest order methods in time discretisation. This approach while straightforward, leads to simulations that require many “cheap” steps. We present abstractions for superstepping as well as more traditional higher order timestepping methods, specifically mutli-stage explicit Runge-Kutta timesteppers. Whilst more expensive to compute, these higher order time discretisations have a larger critical timestep. This allows for advancing propagators more rapidly and obtaining solutions in fewer timesteps at the cost of slightly more compute per timestep.