Algorithm 839: FIAT, a new paradigm for computing finite element basis functions. Much of finite element computation is constrained by the difficulty of evaluating high-order nodal basis functions. While most codes rely on explicit formulae for these basis functions, we present a new approach that allows us to construct a general class of finite element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This approach relies on fundamental ideas from linear algebra and is implemented in Python using several object-oriented and functional programming techniques. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 21 articles , 1 standard article )

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  1. Miklos Homolya, Lawrence Mitchell, Fabio Luporini, David A. Ham: TSFC: a structure-preserving form compiler (2017) arXiv
  2. Robert C. Kirby, Lawrence Mitchell: Solver composition across the PDE/linear algebra barrier (2017) arXiv
  3. Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.: Efficient mesh management in firedrake using PETSc DMPlex (2016)
  4. 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)
  5. Farrell, P.E.; Cotter, C.J.; Funke, S.W.: A framework for the automation of generalized stability theory (2014)
  6. Rognes, Marie E.; Logg, Anders: Automated goal-oriented error control. I: Stationary variational problems (2013)
  7. Russell, Francis P.; Kelly, Paul H.J.: Optimized code generation for finite element local assembly using symbolic manipulation (2013)
  8. Alnæs, Martin Sandve; Mardal, Kent-André: On the efficiency of symbolic computations combined with code generation for finite element methods (2010)
  9. Logg, Anders; Wells, Garth N.: DOLFIN: automated finite element computing (2010)
  10. Long, Kevin; Kirby, Robert; Van Bloemen Waanders, Bart: Unified embedded parallel finite element computations via software-based Fréchet differentiation (2010)
  11. Pena, Gonçalo; Prud’homme, Christophe: Construction of a high order fluid-structure interaction solver (2010)
  12. Rognes, Marie E.; Kirby, Robert C.; Logg, Anders: Efficient assembly of $H(\mathrmdiv)$ and $H(\mathrmcurl)$ conforming finite elements (2009)
  13. Wolf, Michael M.; Heath, Michael T.: Combinatorial optimization of matrix-vector multiplication in finite element assembly (2009)
  14. Terrel, A.R.; Scott, L.R.; Knepley, M.G.; Kirby, R.C.: Automated FEM discretizations for the Stokes equation (2008)
  15. Logg, Anders: Automating the finite element method (2007)
  16. Kirby, Robert C.: Optimizing FIAT with level 3 BLAS. (2006)
  17. Kirby, Robert C.; Knepley, Matthew; Logg, Anders; Scott, L.Ridgway: Optimizing the evaluation of finite element matrices (2005)
  18. Kirby, Robert C.: Algorithm 839: FIAT, a new paradigm for computing finite element basis functions (2004)
  19. Broggi, Alberto; Bertozzi, Massimo; Fascioli, Alessandra; Conte, Gianni: Automatic vehicle guidance. The experience of the ARGO autonomous vehicle (1999)
  20. Vidakovic, Brani; Ruggeri, Fabrizio: Expansion estimation by Bayes rules (1999)

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