2017/03/21 by Matthias Bolten, Bolten, Matthias, Dieter Moser +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1703.07120
openalex publication_date 2017/03/21 · openalex created_date 2022/09/18 · openalex updated_date 2026/07/28
For time-dependent partial differential equations, parallel-in-time\nintegration using the "parallel full approximation scheme in space and time"\n(PFASST) is a promising way to accelerate existing space-parallel approaches\nbeyond their scaling limits. Inspired by the classical Parareal method and\nmultigrid ideas, PFASST allows to integrate multiple time-steps simultaneously\nusing a space-time hierarchy of spectral deferred correction sweeps. While many\nuse cases and benchmarks exist, a solid and reliable mathematical foundation is\nstill missing. Very recently, however, PFASST for linear problems has been\nidentified as multigrid method and in this paper, we will use this multigrid\nformulation and in particular PFASST's iteration matrix to show that in the\nnon-stiff as well as in the stiff limit PFASST indeed is a convergent iterative\nmethod. We will provide upper bounds for the spectral radius of the iteration\nmatrix and investigate how PFASST performs for increasing numbers of parallel\ntime-steps. Finally, we will demonstrate that the results obtained here indeed\nrelate to actual PFASST runs.\n