BIRS Workshop Lecture Videos
Exploiting new degrees of parallelization with rational approximations for linear and non-linear time integration Schreiber, Martin
The current trend in high-performance computing of a stagnating or even decreasing processor speed poses new challenges to solve PDEs within a particular time frame. Here, disruptive mathematical reformulations which exploit additional degrees of parallelism also in the time dimension gained increasing interest over the last two decades. One of such reformulations is a rational approximation of exponential integrators (REXI) which replaces a purely CFL-limited and therefore sequential time integration for linear oscillatory or diffusive systems by a sum of solutions of decoupled systems. Each of the terms in the sum can then be solved independently, hence massively parallel for arbitrarily long time step sizes of linear operators. We will present studies conducted with the linear and non-linear shallow-water equations on the rotating sphere. These equations represent a simplified model of the equations used for weather and climate simulations, but with a focus on horizontal aspects. Various benchmarks will be discussed, including timestepsize-to-error and wallclocktime-to-error, revealing sweet spots of exponential integrators. The results motivate further explorations of REXI for operational weather/climate systems.
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