%0 Generic %1 citeulike:13563213 %A Alnæs, Martin S. %A Logg, Anders %A Ølgaard, Kristian B. %A Rognes, Marie E. %A Wells, Garth N. %D 2013 %K ufl 68n15-programming-languages 65n30-pdes-bvps-finite-elements 35-04-pdes-explicit-machine-computation-programs 35a15-variational-methods-for-pdes 97n80-mathematical-software-computer-programs 65k10-numerical-analysis-optimization-and-variational-techniques fenics %T Unified Form Language: A Domain-Specific Language for Weak Formulations of Partial Differential Equations %U http://arxiv.org/abs/1211.4047 %X 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 multi-field 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.

@misc{citeulike:13563213, abstract = {{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 multi-field 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.}}, added-at = {2017-06-29T07:13:07.000+0200}, archiveprefix = {arXiv}, author = {Aln{\ae}s, Martin S. and Logg, Anders and {\O}lgaard, Kristian B. and Rognes, Marie E. and Wells, Garth N.}, biburl = {https://www.bibsonomy.org/bibtex/20d1004b93d176009b0dc5da58c515304/gdmcbain}, citeulike-article-id = {13563213}, citeulike-attachment-1 = {alnaes_13_unified_1011091.pdf; /pdf/user/gdmcbain/article/13563213/1011091/alnaes_13_unified_1011091.pdf; 440e426f41b3b3e6296a71ef166b0a48ac162ac3}, citeulike-linkout-0 = {http://arxiv.org/abs/1211.4047}, citeulike-linkout-1 = {http://arxiv.org/pdf/1211.4047}, day = 25, eprint = {1211.4047}, file = {alnaes_13_unified_1011091.pdf}, interhash = {2e0787fc41f24a623534e45ca2517138}, intrahash = {0d1004b93d176009b0dc5da58c515304}, keywords = {ufl 68n15-programming-languages 65n30-pdes-bvps-finite-elements 35-04-pdes-explicit-machine-computation-programs 35a15-variational-methods-for-pdes 97n80-mathematical-software-computer-programs 65k10-numerical-analysis-optimization-and-variational-techniques fenics}, month = apr, posted-at = {2015-03-27 04:16:56}, priority = {0}, timestamp = {2023-07-10T08:48:30.000+0200}, title = {Unified {F}orm {L}anguage: A Domain-Specific Language for Weak Formulations of Partial Differential Equations}, url = {http://arxiv.org/abs/1211.4047}, year = 2013 }