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PFASST and Finite Elements

Banff International Research Station for Mathematical Innovation and Discovery

The "parallel full approximation scheme in space and time" (PFASST) is an iterative, multilevel strategy for the temporal parallelization of ODEs and discretized PDEs. In numerous studies, this approach has been successfully coupled to space-parallel solvers which use finite differences, spectral methods or even particles for discretization in space. In this talk, we will report on our experience using PFASST in time together with finite elements in space. In particular, we discuss modifications necessary to treat the mass matrix appropriately on all levels of the space hierarchy and describe a procedure to switch between these levels. For our experiments, the base implementation is the PFASST++ software, a C++ implementation of PFASST and its building blocks MLSDC and SDC. In the context of the finite element discretizations we make use of the "Distributed and Unified Numerics Environment" (DUNE), which is a modular framework for solving PDEs with grid-based methods. Using this coupling of PFASST++ and DUNE, we will show first results for a nonlinear two-component Gray-Scott model. This work is conducted within the project "ParaPhase", where the final goal is the development of a highly scalable space-time parallel adaptive algorithm for the simulation of phase-field models.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: Jülich Supercomputing Centre

2017-10-15

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63287

Unreviewed

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