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A multigrid perspective on PFASST

Banff International Research Station for Mathematical Innovation and Discovery

For time-dependent PDEs, parallel-in-time integration using the "parallel full approximation scheme in space and time" (PFASST) is a promising way to accelerate existing space-parallel approaches beyond their scaling limits. While many use cases and benchmarks exist, a solid and reliable mathematical foundation is still missing. In this talk, we formulate PFASST as a specialized FAS multigrid method. We use spectral deferred corrections for the definition of block smoothers and define the appropriate coarse grid correction to establish a tight link between PFASST and standard multigrid methods, providing an easy access to the mathematical analysis and algorithmic optimization. Using local Fourier analysis, we describe first steps towards a semi-algebraic convergence analysis for the linear case and show some results for diffusive and advective prototype problems.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: Jülich Supercomputing Centre

2017-05-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61648

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/