Colóquio MAP
“Exponential Integrators for Weather and Climate Simulations using Global Spectral Methods”
Dr. Martin Schreiber (University of Exeter)
Dia: 06 de abril, sexta-feira, das 14h. às 15h.
Local: Auditório Antonio Gilioli – Sala 247/262 Bloco A, IME-USP, Café às 15h na sala 265 A (Chefia do MAP).
Abstract:
The current trend in high-performance computing towards many-core systems, increased vector lengths as well as stagnating or even decreasing processor speeds 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). This allows us to replace a purely sequential time integration for linear oscillatory or diffusive systems by a sum of solutions of decoupled system. 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 also include a discussion on using Cauchy contour integral methods to infer the coefficients of such a time integration method. Studies are conducted based on the linear and non-linear shallow-water equations on the rotating sphere. These equations represent a simplified model of the real atmosphere, putting the focus on horizontal aspects. Results on timestepsize-to-error as well as wallclocktime-to-error will be discussed in detail, revealing sweetspots of exponential integrators. The results motivate further explorations of REXI for operational weather/climate systems.
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