Parallel in Time Integration with Rational Approximations targeting Weather and Climate Simulations


Dr. Martin Schreiber
Chair of Computer Architecture and Parallel Systems
Technische Universität München

Project Summary

As part of this KONWIHR funding, we have investigated ways to improve the forecasting with weather simulations as well as an increase of the performance of climate simulations. Such forecasting systems conduct the simulation with a time integration applied in a step-by-step fashion, computing the approximation of the atmosphere based on the state a few minutes or seconds ahead. The time step size between the different states, related to the total number of time steps required for the simulation, is also limited by the resolution. As a consequence, using higher resolutions for, e.g., improved weather forecasts, more and more time steps need to be computed.

A so-called exponential integration formulation allows a time integration without such limitations to the time step size. One way to solve the linear parts of the atmospheric equations can be accomplished by replacing the sequential time integration with a massively parallel rational approximation of exponential integration (REXI). This approach also allows to exploit the high degree of parallelism on current and future super computers.

In this project, we researched REXI methods in different ways: (a) We reformulated the linear solvers to a significantly better ones. (b) We inferred REXI coefficients which lead to a reduction of required computing resources by a factor of 2, therefore possible savings of 50% of the super computers procurement costs if running such simulations with REXI. (c) We compared SuperMUC-NG’s fat tree network with a hypercube one, pointing out a high performance of SuperMUC-NG’s network for REXI methods.

These results and insights will be taken further into account for future developments of REXI-based time integration methods for climate and weather simulations and beyond.