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Parallel strategies for solving the FETI coarse problem in the PERMON toolbox. (English) Zbl 1413.65002

Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 18. Proceedings of the 18th seminar (PANM), Janov nad Nisou, Czech Republic, June 19–24, 2016. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 154-163 (2017).
The paper presents PERMON, a collection of software libraries combining quadratic programming and domain decomposition methods. The main contribution of the paper is proposing and testing two strategies for a parallel solution of the coarse problem arising in the Finite Element Tearing and Interconnecting (FETI) method. The authors compare the time required for the solution of the coarse problem by a parallel sparse direct solver and by a developed technique for computing an explicit inverse of the matrix. The latter approach needs more time in the set-up phase, while it is faster to apply to a vector. Hence, it becomes beneficial for problems requiring many iterations with only one setup.
For the entire collection see [Zbl 1400.65005].

MSC:

65-04 Software, source code, etc. for problems pertaining to numerical analysis
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation
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