
{\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
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)
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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