2019/12/02 by Ruth Schöbel, Schöbel, Ruth, Robert Speck +1 · 1 citation
Computer Science · Mathematics · #Distributed #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Numerical Analysis (math.NA) #Parallel #and Cluster Computing (cs.DC) #cs.DC #cs.MS #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1912.00702
12 pages, 12 figures, CVS PinT Workshop Proceedings
arxiv created 2019/12/02 · arxiv updated 2019/12/03
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to a space-time multigrid, PFASST is able to compute multiple time-steps simultaneously and is therefore in particular suitable for large-scale applications on high performance computing systems. In this work we couple PFASST with a parallel spectral deferred correction (SDC) method, forming an unprecedented doubly time-parallel integrator. While PFASST provides global, large-scale "parallelization across the step", the inner parallel SDC method allows to integrate each individual time-step "parallel across the method" using a diagonalized local Quasi-Newton solver. This new method, which we call "PFASST with Enhanced concuRrency" (PFASST-ER), therefore exposes even more temporal parallelism. For two challenging nonlinear reaction-diffusion problems, we show that PFASST-ER works more efficiently than the classical variants of PFASST and can be used to run parallel-in-time beyond the number of time-steps.