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The Dune framework: basic concepts and recent developments. (English) Zbl 1524.65003

Summary: This paper presents the basic concepts and the module structure of the Distributed and Unified Numerics Environment and reflects on recent developments and general changes that happened since the release of the first Dune version in 2007 and the main papers describing that state [P. Bastian et al., Computing 82, No. 2–3, 103–119 (2008; Zbl 1151.65089); Computing 82, No. 2–3, 121–138 (2008; Zbl 1151.65088)]. This discussion is accompanied with a description of various advanced features, such as coupling of domains and cut cells, grid modifications such as adaptation and moving domains, high order discretizations and node level performance, non-smooth multigrid methods, and multiscale methods. A brief discussion on current and future development directions of the framework concludes the paper.

MSC:

65-04 Software, source code, etc. for problems pertaining to numerical analysis
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35R37 Moving boundary problems for PDEs
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References:

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