UG -- a flexible software toolbox for solving partial differential equations: Over the past two decades, some very efficient techniques for the numerical solution of partial differential equations have been developed. We are especially interested in adaptive local grid refinement on unstructured meshes, multigrid solvers and parallelization techniques. Up to now, these innovative techniques have been implemented mostly in university research codes and only very few commercial codes use them. There are two reasons for this. Firstly, the multigrid solution and adaptive refinement for many engineering applications are still a topic of active research and cannot be considered to be mature enough for routine application. Secondly, the implementation of all these techniques in a code with sufficient generality requires a lot of time and know-how in different fields. UG (abbreviation for Unstructured Grids) has been designed to overcome these problems. It provides very general tools for the generation and manipulation of unstructured meshes in two and three space dimensions as well as a flexible data layout. Therefore, it can serve on the one hand as a tool for exploring new algorithms and, on the other hand, a whole range of algorithms already implemented can be applied to complex problems. In this paper, we show the software design structure of UG and explore some of the subsystems in more detail. Finally, we try to illustrate the capabilities of the approach with several non-trivial examples

References in zbMATH (referenced in 190 articles , 1 standard article )

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  1. Bastian, Peter; Blatt, Markus; Dedner, Andreas; Dreier, Nils-Arne; Engwer, Christian; Fritze, René; Gräser, Carsten; Grüninger, Christoph; Kempf, Dominic; Klöfkorn, Robert; Ohlberger, Mario; Sander, Oliver: The \textscDuneframework: basic concepts and recent developments (2021)
  2. Baumgarten, Niklas; Wieners, Christian: The parallel finite element system M++ with integrated multilevel preconditioning and multilevel Monte Carlo methods (2021)
  3. Sander, Oliver: DUNE -- the distributed and unified numerics environment (2020)
  4. Andreas Nüßing, Maria Carla Piastra, Sophie Schrader, Tuuli Miinalainen, Heinrich Brinck, Carsten H. Wolters, Christian Engwer: duneuro - A software toolbox for forward modeling in neuroscience (2019) arXiv
  5. Grande, Jörg: Red-green refinement of simplicial meshes in (d) dimensions (2019)
  6. Peter Bastian, Markus Blatt, Andreas Dedner, Nils-Arne Dreier, Christian Engwer, René Fritze, Carsten Gräser, Christoph Grüninger, Dominic Kempf, Robert Klöfkorn, Mario Ohlberger, Oliver Sander: The DUNE Framework: Basic Concepts and Recent Developments (2019) arXiv
  7. Dong, Justin; Rivière, Béatrice: A semi-implicit method for incompressible three-phase flow in porous media (2016)
  8. Frolkovič, Peter; Lampe, Michael; Wittum, Gabriel: Numerical simulation of contaminant transport in groundwater using software tools of (r^3t) (2016)
  9. Frolkovič, Peter; Logashenko, Dmitriy; Wehner, Christian: Flux-based level-set method for two-phase flows on unstructured grids (2016)
  10. Krause, Rolf; Rigazzi, Alessandro; Steiner, Johannes: A parallel multigrid method for constrained minimization problems and its application to friction, contact, and obstacle problems (2016)
  11. Maurer, Daniel; Wieners, Christian: A scalable parallel factorization of finite element matrices with distributed Schur complements. (2016)
  12. de Cuveland, Rebecca: Two-phase compositional flow simulation with persistent variables (2015)
  13. Hauser, Andreas; Wittum, G.: Adaptive large eddy simulation (2015)
  14. Krause, Rolf; Veeser, Andreas; Walloth, Mirjam: An efficient and reliable residual-type a posteriori error estimator for the Signorini problem (2015)
  15. Ngo, A. Q. T.; Bastian, P.; Ippisch, O.: Numerical solution of steady-state groundwater flow and solute transport problems: discontinuous Galerkin based methods compared to the streamline diffusion approach (2015)
  16. Bastian, Peter: A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure (2014)
  17. Dickopf, Thomas; Krause, Dorian; Krause, Rolf; Potse, Mark: Design and analysis of a lightweight parallel adaptive scheme for the solution of the monodomain equation (2014)
  18. Geiser, Juergen: Coupled systems. Theory, models, and applications in engineering (2014)
  19. Krause, Dorian; Fackeldey, Konstantin; Krause, Rolf: A parallel multiscale simulation toolbox for coupling molecular dynamics and finite elements (2014)
  20. Matveenko, V. P.; Shardakov, I. N.; Shestakov, A. P.; Wasserman, I. N.: Development of finite element models for studying the electrical excitation of myocardium (2014)

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