UFL swMATH ID: 11183 Software Authors: Alnæs, Martin S.; Logg, Anders; Ølgaard, Kristian B.; Rognes, Marie E.; Wells, Garth N. Description: Unified form language: a domain-specific language for weak formulations of partial differential equations. We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies for multifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. Homepage: http://dl.acm.org/citation.cfm?doid=2594412.2566630 Keywords: AD; DSEL; DSL; FEM; PDE; algorithmic differentiation; automatic functional differentiation; discretization; domain specific language; Einstein notation; embedded language; finite element method; functional; implicit summation; index notation; mixed element; partial differential equation; symbolic differentiation; tensor algebra; weak form; weak formulation Related Software: FEniCS; PETSc; Firedrake; DOLFIN; FIAT; SyFi; petsc4py; TSFC; Python; Gmsh; FFC; mpi4py; COFFEE; deal.ii; GitHub; MUMPS; DUNE; PyOP2; UMFPACK; hypre Cited in: 73 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Unified form language: a domain-specific language for weak formulations of partial differential equations. Zbl 1308.65175Alnæs, Martin S.; Logg, Anders; Ølgaard, Kristian B.; Rognes, Marie E.; Wells, Garth N. 2014 all top 5 Cited by 163 Authors 6 Mitchell, Lawrence 5 Cotter, Colin John 5 Kamensky, David 5 Rognes, Marie Elisabeth 4 Dedner, Andreas S. 4 Farrell, Patrick E. 4 Funke, Simon W. 4 Ham, David A. 4 Kirby, Robert C. 3 Bazilevs, Yuri 3 Breckling, Sean 3 Klöfkorn, Robert 3 Larson, Mats G. 3 Logg, Anders 3 Maddison, James R. 3 Massing, André 3 McRae, Andrew T. T. 3 Nakshatrala, Kalyana B. 3 Schmidt, Stephan 2 Bordas, Stéphane Pierre Alain 2 Budd, Christopher John 2 Farrell, Patrick Emmet 2 Gibson, Thomas H. 2 Hale, Jack S. 2 Joodat, S. H. S. 2 Luporini, Fabio 2 Müller, Eike Hermann 2 Neda, Monika 2 Potschka, Andreas 2 Wathen, Andrew John 2 Wells, Garth N. 1 Adriaenssens, Sigrid 1 Ahlkrona, Josefin 1 Alnæs, Martin Sandve 1 Anitescu, Cosmin 1 Ausas, Roberto Federico 1 Ballarini, Roberto 1 Baroli, Davide 1 Bastian, Peter 1 Beex, Lars A. A. 1 Bercea, Gheorghe-Teodor 1 Bergmann, Ronny 1 Betteridge, Jack 1 Blatt, Markus 1 Blechta, Jan 1 Bock, Hans Georg 1 Boullé, Nicolas 1 Burman, Erik 1 Buscaglia, Gustavo Carlos 1 Cao, Jian 1 Chang, Justin 1 Claus, Susanne 1 Dreier, Nils-Arne 1 Dubos, Thomas 1 Dunning, Iain 1 Ehmann, Kornel 1 Eldred, Christopher 1 Engwer, Christian 1 Evans, John A. 1 Fletcher, Andrew H. 1 Fritze, René 1 Gajardo, Diego 1 Gebhardt, Cristian Guillermo 1 Gillette, Andrew 1 Goddard, Benjamin D. 1 Goldberg, Daniel N. 1 Gorman, Gerard J. 1 Goswami, Somdatta 1 Graham, Ivan G. 1 Gräser, Carsten 1 Grüninger, Christoph 1 Guo, Hongwei 1 Hake, J. E. 1 Hamdia, Khader M. 1 Hansbo, Peter 1 Hauseux, Paul 1 Helanow, Christian 1 Herrmann, Marc 1 Herzog, Roland 1 Hiester, H. R. 1 Homolya, Miklós 1 Hron, Jaroslav 1 Huchette, Joey 1 Hwang, John T. 1 Jahn, Mischa 1 Jönsthövel, Tom B. 1 Joshaghani, M. S. 1 Kane, Birane 1 Katz, Richard F. 1 Kelly, Paul H. J. 1 Kempf, Dominic 1 Kernell, Tate 1 Kincl, Ondřej 1 Kirches, Christian 1 Klöckner, Andreas 1 Kloefkorn, Tyler 1 Knepley, Matthew G. 1 Koutsourelakis, Phaedon-Stelios 1 Kowalski, Julia 1 Kritsikis, Evaggelos ...and 63 more Authors all top 5 Cited in 27 Serials 18 SIAM Journal on Scientific Computing 12 Computer Methods in Applied Mechanics and Engineering 8 Journal of Computational Physics 7 Computers & Mathematics with Applications 2 ACM Transactions on Mathematical Software 2 Applied Mathematical Modelling 2 Computational Geosciences 2 SMAI Journal of Computational Mathematics 1 Computer Physics Communications 1 Inverse Problems 1 Journal of Mathematical Analysis and Applications 1 Applied Mathematics and Computation 1 International Journal for Numerical Methods in Engineering 1 Numerische Mathematik 1 Quarterly of Applied Mathematics 1 SIAM Journal on Control and Optimization 1 Journal of Scientific Computing 1 International Journal of Computer Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Review 1 Mathematical Programming. 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Series B 1 Optimization Methods & Software 1 Communications in Nonlinear Science and Numerical Simulation 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 International Journal of Advances in Engineering Sciences and Applied Mathematics 1 Communications on Applied Mathematics and Computation 1 Journal of Computational and Theoretical Transport all top 5 Cited in 18 Fields 57 Numerical analysis (65-XX) 28 Fluid mechanics (76-XX) 19 Partial differential equations (35-XX) 13 Mechanics of deformable solids (74-XX) 11 Computer science (68-XX) 9 Geophysics (86-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Operations research, mathematical programming (90-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year