A multigrid perspective on the parallel full approximation scheme in space and time. Issue 6 (8th June 2017)

• Record Type: Journal Article
• Authors: Bolten, Matthias; Moser, Dieter; Speck, Robert
• Is Part Of: Numerical linear algebra with applications. Volume 24:Issue 6(2017:Nov.)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2017-06-08
• Subjects: high‐performance computing -- local Fourier analysis -- multigrid -- parallel‐in‐time -- PFASST; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2110
• Languages: English
• ISSNs: 1070-5325

Abstract

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.