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ParMooN—A modernized program package based on mapped finite elements

ParMooN -- a modernized program package based on mapped finite elements
Authors: Wilbrandt, Ulrich; Bartsch, Clemens; Ahmed, Naveed; Alia, Najib; Anker, Felix; Blank, Laura; Caiazzo, Alfonso; +7 Authors

ParMooN—A modernized program package based on mapped finite elements

Abstract

{\sc ParMooN} is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierarchy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of {\sc ParMooN}. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library {\sc PETSc}. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.

partly supported by European Union (EU), Horizon 2020, Marie Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant number 675715

Keywords

Geometric multigrid method, FOS: Computer and information sciences, Multigrid methods; domain decomposition for boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, mapped finite elements, 510, Boundary value problems for second-order elliptic equations, program package, Mapped finite elements -- Geometric multigrid method -- Parallelization, Initial-boundary value problems for second-order parabolic equations, parallelization, 65Y05, FOS: Mathematics, Mathematics - Numerical Analysis, geometric multigrid method, ddc:510, numerical examples, 000, article, Parallelization, Parallel numerical computation, Numerical Analysis (math.NA), Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs, \textsc{ParMooN}, Packaged methods for numerical algorithms, Computer Science - Mathematical Software, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mapped finite elements, Mathematical Software (cs.MS)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
43
Top 10%
Top 10%
Top 10%
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