Today's supercomputers already feature millions of cores and this number is anticipated to rise to more than 100 million over the next decade. Computational Science therefore has to come up with novel numerical methods that can provide the required concurrency. Parallel-in-time methods like Parareal or PFASST are attractive candidates to add an additional direction of parallelization on top of already established strategies for parallelization in space. Researchers at ICS are working on different methods, their analysis and application and strategies for their benchmarking and efficient implementation on modern high-performance computing installations.
Solution computed with Parareal for a diffusion problem with spatially varying coefficients [Ruprecht et al. 2014]. The varying coefficients do not significantly impact the good convergence of Parareal for constant-coefficient diffusion problems shown e.g. in [Gander, Vandewalle 2007].
In [Kreienbuehl et al. 2015] we test the applicability of the Parareal method to the numerical solution of the Einstein gravity equations in the case of a black hole formation. Our experiments show that Parareal generates substantial speedup and can reproduces expected physical results.
Solution of a time-periodic fluid flow problem [Benedusi et al. 2015], computed with a space-time multigrid approach that can be parallelized in all dimensions. This project was a collaboration with Prof. Peter Arbenz and Daniel Hupp in ETH Zürich.
Advisor Rolf Krause
Researcher Pietro Benedusi, Xiaozhou Li
X. Li, P. Benedusi, R. Krause, "An Iterative Approach for Time Integration Based on 2 Discontinuous Galerkin Methods", under revision.;