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 56 articles , 1 standard article )

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  1. Bastian, Peter; Blatt, Markus; Dedner, Andreas; Dreier, Nils-Arne; Engwer, Christian; Fritze, René; Gräser, Carsten; Grüninger, Christoph; Kempf, Dominic; Klöfkorn, Robert; Ohlberger, Mario; Sander, Oliver: The \textscDuneframework: basic concepts and recent developments (2021)
  2. Gajardo, Diego; Mercado, Alberto; Muñoz, Juan Carlos: Identification of the anti-diffusion coefficient for the linear Kuramoto-Sivashinsky equation (2021)
  3. Kamensky, David: Open-source immersogeometric analysis of fluid-structure interaction using FEniCS and tIGAr (2021)
  4. Kirby, Robert C.; Kernell, Tate: Preconditioning mixed finite elements for tide models (2021)
  5. Zimmerman, Alexander G.; Kowalski, Julia: Mixed finite elements for convection-coupled phase-change in enthalpy form: open software verified and applied to 2D benchmarks (2021)
  6. Bazilevs, Yuri; Kamensky, David; Moutsanidis, Georgios; Shende, Shaunak: Residual-based shock capturing in solids (2020)
  7. Dedner, Andreas; Klöfkorn, Robert: A Python framework for solving advection-diffusion problems (2020)
  8. Evans, John A.; Kamensky, David; Bazilevs, Yuri: Variational multiscale modeling with discretely divergence-free subscales (2020)
  9. Jahn, Mischa; Montalvo-Urquizo, Jonathan: Modeling and simulation of keyhole-based welding as multi-domain problem using the extended finite element method (2020)
  10. Roy, Thomas; Jönsthövel, Tom B.; Lemon, Christopher; Wathen, Andrew J.: A constrained pressure-temperature residual (CPTR) method for non-isothermal multiphase flow in porous media (2020)
  11. Samaniego, E.; Anitescu, C.; Goswami, S.; Nguyen-Thanh, V. M.; Guo, H.; Hamdia, K.; Zhuang, X.; Rabczuk, Timon: An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications (2020)
  12. Breckling, Sean; Shields, Sidney: The long-time (L^2) and (H^1) stability of linearly extrapolated second-order time-stepping schemes for the 2D incompressible Navier-Stokes equations (2019)
  13. Dedner, Andreas; Kane, Birane; Klöfkorn, Robert; Nolte, Martin: Python framework for hp-adaptive discontinuous Galerkin methods for two-phase flow in porous media (2019)
  14. Farrell, Patrick E.; Mitchell, Lawrence; Wechsung, Florian: An augmented Lagrangian preconditioner for the 3D stationary incompressible Navier-Stokes equations at High Reynolds number (2019)
  15. Farrell, P. E.; Hake, J. E.; Funke, S. W.; Rognes, M. E.: Automated adjoints of coupled PDE-ODE systems (2019)
  16. Gillette, Andrew; Kloefkorn, Tyler; Sanders, Victoria: Computational serendipity and tensor product finite element differential forms (2019)
  17. Joshaghani, M. S.; Joodat, S. H. S.; Nakshatrala, K. B.: A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model (2019)
  18. Kamensky, David; Bazilevs, Yuri: \textsctIGAr: automating isogeometric analysis with \textscFEniCS (2019)
  19. Maddison, James R.; Goldberg, Daniel N.; Goddard, Benjamin D.: Automated calculation of higher order partial differential equation constrained derivative information (2019)
  20. Winovich, Nick; Ramani, Karthik; Lin, Guang: ConvPDE-UQ: convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains (2019)

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