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 169 articles , 1 standard article )

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  1. Frolkovič, Peter; Lampe, Michael; Wittum, Gabriel: Numerical simulation of contaminant transport in groundwater using software tools of $r^3t$ (2016)
  2. Frolkovič, Peter; Logashenko, Dmitriy; Wehner, Christian: Flux-based level-set method for two-phase flows on unstructured grids (2016)
  3. Krause, Rolf; Rigazzi, Alessandro; Steiner, Johannes: A parallel multigrid method for constrained minimization problems and its application to friction, contact, and obstacle problems (2016)
  4. de Cuveland, Rebecca: Two-phase compositional flow simulation with persistent variables (2015)
  5. Krause, Rolf; Veeser, Andreas; Walloth, Mirjam: An efficient and reliable residual-type a posteriori error estimator for the Signorini problem (2015)
  6. 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)
  7. Geiser, Juergen: Coupled systems. Theory, models, and applications in engineering (2014)
  8. Krause, Dorian; Fackeldey, Konstantin; Krause, Rolf: A parallel multiscale simulation toolbox for coupling molecular dynamics and finite elements (2014)
  9. 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)
  10. Kumar, K.; Pop, I.S.; Radu, F.A.: Convergence analysis of mixed numerical schemes for reactive flow in a porous medium (2013)
  11. Kumar, K.; Pop, I.S.; Radu, F.A.: Numerical analysis for an upscaled model for dissolution and precipitation in porous media (2013)
  12. Nicolas, Gérald; Fouquet, Thierry: Adaptive mesh refinement for conformal hexahedralmeshes (2013)
  13. Radu, Florin A.; Muntean, Adrian; Pop, Iuliu S.; Suciu, Nicolae; Kolditz, Olaf: A mixed finite element discretization scheme for a concrete carbonation model with concentration-dependent porosity (2013)
  14. Ray, Nadja; van Noorden, Tycho; Radu, Florin; Friess, Wolfgang.; Knabner, Peter: Drug release from collagen matrices including an evolving microstructure (2013)
  15. Hüeber, Stefan; Wohlmuth, Barbara I.: Equilibration techniques for solving contact problems with Coulomb friction (2012)
  16. Krause, Rolf; Walloth, Mirjam: Presentation and comparison of selected algorithms for dynamic contact based on the Newmark scheme (2012)
  17. Berninger, Heiko; Kornhuber, Ralf; Sander, Oliver: Fast and robust numerical solution of the Richards equation in homogeneous soil (2011)
  18. Fackeldey, Konstantin; Krause, Dorian; Krause, Rolf: Numerical validation of a constraints-based multiscale simulation method for solids (2011)
  19. Fackeldey, Konstantin; Krause, Dorian; Krause, Rolf; Lenzen, Christoph: Coupling molecular dynamics and continua with weak constraints (2011)
  20. Geiser, J.; Arab, M.: Modeling and simulation of a chemical vapor deposition (2011)

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