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
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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

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