## UG

 swMATH ID: 4596 Software Authors: Bastian, P.; Birken, K.; Johannsen, K.; Lang, S.; Neuß, N.; Rentz-Reichert, H.; Wieners, C. Description: 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 Homepage: http://atlas.gcsc.uni-frankfurt.de/~ug/ Keywords: software toolbox; numerical examples; adaptive local grid refinement; unstructured meshes; multigrid; parallelization; unstructured grids; algorithms Related Software: DUNE; PETSc; PLTMG; deal.ii; UMFPACK; Diffpack; COUPLEX; ALBERTA; ISTL; Kaskade7; Trilinos; libMesh; Gmsh; DUNE-ALUGrid; Amira; DDD; PARDISO; ZIBAmira; UG4; MPI Cited in: 177 Publications Further Publications: http://atlas.gcsc.uni-frankfurt.de/~ug/papers.html
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### Cited by 203 Authors

 23 Wohlmuth, Barbara I. 21 Wittum, Gabriel 19 Krause, Rolf H. 18 Wieners, Christian 17 Bastian, Peter 12 Radu, Florin Adrian 11 Pop, Iuliu Sorin 9 Geiser, Jürgen 9 Hüeber, Stefan 9 Sander, Oliver 6 Lamichhane, Bishnu Prasad 6 Neuss, Nicolas 5 Frolkovič, Peter 5 Knabner, Peter 5 Lang, Stefan M. 5 Logashenko, Dmitry 4 Birken, Klaus 4 Engwer, Christian 4 Johannsen, Klaus 4 Klöfkorn, Robert 4 Kornhuber, Ralf 4 Krause, Dorian 4 Ohlberger, Mario 4 Reichenberger, Volker 4 Schulz, Volker H. 4 Walloth, Mirjam 3 Attinger, Sabine 3 Dedner, Andreas S. 3 Deuflhard, Peter 3 Eberhard, Jens P. 3 Fackeldey, Konstantin 3 Groß, Sven 3 Hauser, Andreas 3 Maar, Bernd 3 Reusken, Arnold 3 Wrobel, Christian 2 Banaś, Krzysztof 2 Baron, Romain 2 Bause, Markus 2 Berninger, Heiko 2 Blatt, Markus 2 Dickopf, Thomas 2 Friess, Wolfgang 2 Gräser, Carsten 2 Hager, Corinna 2 Heineken, Wolfram 2 Illangasekare, Tissa H. 2 John, Volker 2 Kempf, Dominic 2 Klapproth, Corinna 2 Kumar, Kundan 2 Lampe, Michael 2 Liu, Weiming 2 Mair, Michael 2 Marpeau, Fabien 2 Mikyška, jiří 2 Paxion, S. 2 Plum, Michael 2 Sterz, Oliver 2 Wagner, Christian 2 Warnecke, Gerald G. 1 Ammann, Martin 1 Anwander, Alfred 1 Apoung Kamga, Jean-Baptiste 1 Athale, Chaitanya A. 1 Bank, Randolph E. 1 Baumgarten, Niklas 1 Beck, Rudolf 1 Bertolazzi, Enrico 1 Braess, Dietrich 1 Buck, V. 1 Buzdin, A. A. 1 Cai, Xing 1 Carey, Graham Francis 1 Chavan, K. S. 1 Chen, Zhangxin 1 Čiegis, Raimondas 1 Dahmen, Wolfgang A. 1 de Cuveland, Rebecca 1 Després, Bruno 1 Diebels, Stefan 1 Dimkić, Milan 1 Dong, Justin 1 Dooley, Isaac 1 Dreier, Nils-Arne 1 Dreyer, Thomas 1 Droske, Marc 1 Ehlers, Wolfgang 1 Eigel, Martin 1 Eils, Roland 1 Erdmann, Bodo 1 Ewing, Richard Edward 1 Falcke, Martin 1 Fischer, Torsten 1 Fleck, Christian 1 Fouquet, Thierry 1 Fritze, René 1 Geubelle, Philippe H. 1 Gicquel, Olivier 1 Gordner, Achim ...and 103 more Authors
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### Cited in 45 Serials

 23 Computing and Visualization in Science 9 Computer Methods in Applied Mechanics and Engineering 9 SIAM Journal on Numerical Analysis 8 Numerische Mathematik 8 SIAM Journal on Scientific Computing 6 Journal of Computational Physics 6 Computing 6 Journal of Computational and Applied Mathematics 5 Applied Numerical Mathematics 5 Computational Geosciences 4 International Journal for Numerical Methods in Fluids 3 International Journal for Numerical Methods in Engineering 2 Computers & Mathematics with Applications 2 Mathematics of Computation 2 ACM Transactions on Mathematical Software 2 Numerical Methods for Partial Differential Equations 2 Journal of Scientific Computing 2 Numerical Linear Algebra with Applications 2 Mathematical Problems in Engineering 2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 2 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 2 Multiscale Modeling & Simulation 1 Acta Mechanica 1 Journal of Engineering Mathematics 1 Journal of Mathematical Analysis and Applications 1 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 1 Calcolo 1 Kybernetika 1 Mathematics and Computers in Simulation 1 Finite Elements in Analysis and Design 1 Computational Mechanics 1 Acta Mathematica Universitatis Comenianae. New Series 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 International Journal of Computer Mathematics 1 Communications in Numerical Methods in Engineering 1 Turkish Journal of Mathematics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Multibody System Dynamics 1 Mathematical Modelling and Analysis 1 Journal of Applied Mathematics 1 Lecture Notes in Mathematics 1 Springer Series in Computational Mathematics 1 Lecture Notes in Computational Science and Engineering 1 International Mathematical Forum 1 Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
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### Cited in 20 Fields

 127 Numerical analysis (65-XX) 69 Fluid mechanics (76-XX) 55 Partial differential equations (35-XX) 48 Mechanics of deformable solids (74-XX) 13 Biology and other natural sciences (92-XX) 9 Computer science (68-XX) 9 Classical thermodynamics, heat transfer (80-XX) 6 Geophysics (86-XX) 4 Mechanics of particles and systems (70-XX) 4 Optics, electromagnetic theory (78-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Systems theory; control (93-XX)