Premium
A multigrid perspective on the parallel full approximation scheme in space and time
Author(s) -
Bolten Matthias,
Moser Dieter,
Speck Robert
Publication year - 2017
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2110
Subject(s) - multigrid method , partial differential equation , mathematics , equivalence (formal languages) , spacetime , scaling , perspective (graphical) , space time , numerical analysis , mathematical optimization , algorithm , computer science , mathematical analysis , geometry , discrete mathematics , physics , quantum mechanics , chemical engineering , engineering
Summary For the numerical solution of time‐dependent partial differential equations, time‐parallel methods have recently been shown to provide a promising way to extend prevailing strong‐scaling limits of numerical codes. One of the most complex methods in this field is the “Parallel Full Approximation Scheme in Space and Time” (PFASST). PFASST already shows promising results for many use cases and benchmarks. However, a solid and reliable mathematical foundation is still missing. We show that, under certain assumptions, the PFASST algorithm can be conveniently and rigorously described as a multigrid‐in‐time method. Following this equivalence, first steps towards a comprehensive analysis of PFASST using blockwise local Fourier analysis are taken. The theoretical results are applied to examples of diffusive and advective type.