UFL

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.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 29 articles , 1 standard article )

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  1. Breckling, Sean; Neda, Monika; Pahlevani, Fran: A sensitivity study of the Navier-Stokes-(\alpha) model (2018)
  2. Helanow, Christian; Ahlkrona, Josefin: Stabilized equal low-order finite elements in ice sheet modeling -- accuracy and robustness (2018)
  3. Homolya, Miklós; Mitchell, Lawrence; Luporini, Fabio; Ham, David A.: TSFC: a structure-preserving form compiler (2018)
  4. Lenders, Felix; Kirches, C.; Potschka, A.: \texttttrlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem (2018)
  5. McRae, Andrew T. T.; Cotter, Colin J.; Budd, Chris J.: Optimal-transport -- based mesh adaptivity on the plane and sphere using finite elements (2018)
  6. Schmidt, Stephan: Weak and strong form shape hessians and their automatic generation (2018)
  7. Schmidt, Stephan; Schütte, Maria; Walther, Andrea: Efficient numerical solution of geometric inverse problems involving Maxwell’s equations using shape derivatives and automatic code generation (2018)
  8. Dunning, Iain; Huchette, Joey; Lubin, Miles: JuMP: a modeling language for mathematical optimization (2017)
  9. Luporini, Fabio; Ham, David A.; Kelly, Paul H. J.: An algorithm for the optimization of finite element integration loops (2017)
  10. Maddison, J. R.; Hiester, H. R.: Optimal constrained interpolation in mesh-adaptive finite element modeling (2017)
  11. Meftahi, Houcine: Optimal shape design in three-dimensional Brinkman flow using asymptotic analysis techniques (2017)
  12. Miklos Homolya, Lawrence Mitchell, Fabio Luporini, David A. Ham: TSFC: a structure-preserving form compiler (2017) arXiv
  13. Řehoř, Martin; Blechta, Jan; Souček, Ondřej: On some practical issues concerning the implementation of Cahn-Hilliard-Navier-Stokes type models (2017)
  14. Robert C. Kirby, Lawrence Mitchell: Solver composition across the PDE/linear algebra barrier (2017) arXiv
  15. Bauman, Paul T.; Stogner, Roy H.: GRINS: a multiphysics framework based on the libMesh finite element library (2016) ioport
  16. Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.: Efficient mesh management in firedrake using PETSc DMPlex (2016)
  17. McRae, A. T. T.; Bercea, G.-T.; Mitchell, L.; Ham, D. A.; Cotter, C. J.: Automated generation and symbolic manipulation of tensor product finite elements (2016)
  18. Mitchell, Lawrence; Müller, Eike Hermann: High level implementation of geometric multigrid solvers for finite element problems: applications in atmospheric modelling (2016)
  19. Burman, Erik; Claus, Susanne; Hansbo, Peter; Larson, Mats G.; Massing, André: CutFEM: discretizing geometry and partial differential equations (2015)
  20. Mortensen, Mikael; Valen-Sendstad, Kristian: Oasis: a high-level/high-performance open source Navier-Stokes solver (2015)

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