DUNE-FEM swMATH ID: 3084 Software Authors: Dedner, Andreas; Klöfkorn, Robert; Nolte, Martin; Ohlberger, Mario Description: A generic interface for parallel and adaptive discretization schemes: Abstraction principles and the DUNE-FEM module. Starting from an abstract mathematical notion of discrete function spaces and operators, we derive a general abstraction for a large class of grid-based discretization schemes for stationary and instationary partial differential equations. Special emphasis is put on concepts for local adaptivity and parallelization with dynamic load balancing. The concepts are based on a corresponding abstract definition of a parallel and hierarchical adaptive grid given in [{it P. Bastian} et al., Computing 82, No. 2–3, 103–119 (2008; Zbl 1151.65089)]. Based on the abstract framework, we describe an efficient object oriented implementation of a generic interface for grid-based discretization schemes that is realized in the Dune-Fem library (url{http://dune.mathematik.uni-freiburg.de}). By using interface classes, we manage to separate functionality from data structures. Efficiency is obtained by using modern template based generic programming techniques, including static polymorphism, the engine concept, and template metaprogramming. We present numerical results for several benchmark problems and some advanced applications. Homepage: https://www.dune-project.org/about/dune/ Keywords: DUNE; finite elements; finite volumes; discontinuous Galerkin; software; abstract interface; generic programming; C++; parallelization; adaptive methods; dynamic load balancing Related Software: DUNE; deal.ii; PETSc; FEniCS; Feel++; UFL; libMesh; Trilinos; UMFPACK; ALUGrid; ISTL; Dune-FemPy; Python; DUNE-FEM-DG; ParaView; hypre; Getfem++; DOLFIN; MUMPS; FreeFem++ Cited in: 39 Publications Further Publications: https://www.dune-project.org/about/publications/ all top 5 Cited by 90 Authors 10 Dedner, Andreas S. 7 Klöfkorn, Robert 4 Elliott, Charles M. 4 Ohlberger, Mario 3 Nolte, Martin 2 Bastian, Peter 2 Chabannes, Vincent 2 Djurdjevac, Ana 2 Giesselmann, Jan 2 Henning, Patrick 2 Ismail, Mourad 2 Kane, Birane 2 Mansour, Dhia 2 Prud’homme, Christophe 2 Pryer, Tristan 1 Agnese, Marco 1 Ahmed, Naveed 1 Ali, Ijaz 1 Alia, Najib 1 Anker, Felix 1 Bartsch, Clemens 1 Blank, Laura 1 Brdar, Slavko 1 Brett, Charles 1 Burbulla, Samuel 1 Caiazzo, Alfonso 1 Caldini-Queiros, Céline 1 Church, Lewis 1 Doyeux, Vincent 1 Dunbar, Oliver R. A. 1 Efendiev, Yalchin R. 1 Flemisch, Bernd 1 Fritz, Hans 1 Ganesan, Sashikumaar 1 Gerstenberger, Janick 1 Giere, Swetlana 1 Haasdonk, Bernard 1 Heimann, Felix 1 Hobbs, Graham 1 Hu, Qiya 1 John, Volker 1 Kaulmann, Sven 1 Kormann, Katharina 1 Kornhuber, Ralf 1 Kovács, Balázs 1 Kronbichler, Martin 1 Kröner, Dietmar 1 Kronsbein, Cornelia 1 Kvashchuk, Anna 1 Lam, Kei Fong 1 Legoll, Frédéric 1 Liang, Guoping 1 Lie, Knut-Andreas 1 Ling, Siqi 1 Lubich, Christian 1 Madhavan, Pravin 1 Manzoni, Andrea 1 Marnach, Sven 1 Matthies, Gunar 1 Meesala, Raviteja 1 Mitchell, Lawrence 1 Muhammad, Wazir 1 Müller, Eike Hermann 1 Müller, Thomas 1 Munch, Peter 1 Negri, Federico 1 Nürnberg, Robert 1 Pena, Gonçalo 1 Power Guerra, Christian Andreas 1 Praetorius, Simon 1 Quarteroni, Alfio M. 1 Ranner, Thomas 1 Roberts, Nathan V. 1 Ryan, Jennifer K. 1 Sabir, Muhammad Farooq 1 Samake, Abdoulaye 1 Schindler, Felix 1 Schweizer, Ben 1 Shah, Abdullah 1 Shamim, Abdus 1 Stinner, Bjorn 1 Sun, Pengtao 1 Szopos, Marcela 1 Tarabay, Ranine 1 Venkatesan, Jagannath 1 Voigt, Axel 1 Walker, Shawn W. 1 Wilbrandt, Ulrich 1 Witkowski, Thomas 1 Zhou, Su all top 5 Cited in 23 Serials 4 Numerische Mathematik 3 SIAM Journal on Scientific Computing 2 Computers & Mathematics with Applications 2 Mathematics of Computation 2 Journal of Scientific Computing 2 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 2 Multiscale Modeling & Simulation 2 Communications on Applied Mathematics and Computation 1 Journal of Computational Physics 1 ACM Transactions on Mathematical Software 1 Computing 1 International Journal for Numerical Methods in Engineering 1 Kybernetika 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematical Modelling 1 Advances in Computational Mathematics 1 Interfaces and Free Boundaries 1 Computational Geosciences 1 Computational Methods in Applied Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Unitext 1 Communications in Computational Physics 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Cited in 11 Fields 36 Numerical analysis (65-XX) 22 Partial differential equations (35-XX) 14 Fluid mechanics (76-XX) 4 Computer science (68-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Geophysics (86-XX) 2 Biology and other natural sciences (92-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year