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Description

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.