2016/03/11 by Matthias Bolten, Bolten, Matthias, Dieter Moser +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1603.03586
openalex publication_date 2016/03/11 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
For the numerical solution of time-dependent partial differential equations,\ntime-parallel methods have recently shown to provide a promising way to extend\nprevailing strong-scaling limits of numerical codes. One of the most complex\nmethods in this field is the "Parallel Full Approximation Scheme in Space and\nTime" (PFASST). PFASST already shows promising results for many use cases and\nmany more is work in progress. However, a solid and reliable mathematical\nfoundation is still missing. We show that under certain assumptions the PFASST\nalgorithm can be conveniently and rigorously described as a multigrid-in-time\nmethod. Following this equivalence, first steps towards a comprehensive\nanalysis of PFASST using block-wise local Fourier analysis are taken. The\ntheoretical results are applied to examples of diffusive and advective type.\n