The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
Unified form language: A domain-specific language for weak formulations of partial differential equations
Open accessAbstract
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.
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Cited by
Samaniego, E., Anitescu, C., Goswami, S., Nguyen-Thanh, V. M., Guo, H., Hamdia, K., Zhuang, X., & Rabczuk, T. (2020) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2019.112790 · Cited by 2,104
JuMP: A Modeling Language for Mathematical Optimization
Dunning, I., Huchette, J., & Lubin, M. (2017) · SIAM Review · doi:10.1137/15m1020575 · Cited by 1,250
Firedrake: Automating the Finite Element Method by Composing Abstractions
Rathgeber, F., Ham, D. A., Mitchell, L., Lange, M., Luporini, F., Mcrae, A. T. T., Bercea, G.-T., Markall, G. R., & Kelly, P. H. J. (2017) · ACM Transactions on Mathematical Software · doi:10.1145/2998441 · Cited by 508
dolfin-adjoint 2018.1: automated adjoints for FEniCS and Firedrake
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A framework for automated PDE-constrained optimisation
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Metadata
- Authors
- Alnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., & Wells, G. N.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 2014-02
- Volume
- 40
- Issue
- 2
- Pages
- 1-37
- ISSN
- 0098-3500 (ISSN-L)
- 1557-7295
- OpenAlex
- W2107979247
- Cited by
- 615
- References
- 33
- FWCI
- 17.88
- Type
- journal article
- Language
- en
- Open access
- green
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- Alnæs, M. S., Logg, A., Ølgaard, K. B., Rognes, M. E., & Wells, G. N. (2014). Unified form language: A domain-specific language for weak formulations of partial differential equations. ACM Transactions on Mathematical Software. https://doi.org/10.1145/2566630
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