FIAT swMATH ID: 287 Software Authors: Kirby, Robert C. Description: 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. Homepage: http://dl.acm.org/citation.cfm?id=1039820 Related Software: FEniCS; DOLFIN; PETSc; UFL; Firedrake; FFC; deal.ii; FreeFem++; SyFi; Gmsh; TSFC; Python; COFFEE; hypre; petsc4py; Trilinos; Sundance; MUMPS; PyOP2; FIAT Cited in: 45 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 839: FIAT, a new paradigm for computing finite element basis functions. Zbl 1070.65571Kirby, Robert C. 2004 all top 5 Cited by 86 Authors 9 Mitchell, Lawrence 8 Kirby, Robert C. 5 Logg, Anders 4 Knepley, Matthew G. 3 Cotter, Colin John 3 Ham, David A. 2 Bercea, Gheorghe-Teodor 2 Calo, Victor Manuel 2 Dehghan Takht Fooladi, Mehdi 2 Hale, Jack S. 2 Kelly, Paul H. J. 2 Labanda, Nicolás A. 2 Lange, Michael 2 Luporini, Fabio 2 McRae, Andrew T. T. 2 Rognes, Marie E. 2 Sabouri, Mania 2 Scott, Larkin Ridgway 1 Adams, Mark F. 1 Alnæs, Martin Sandve 1 Baiz, P. M. 1 Behnoudfar, Pouria 1 Bertozzi, Massimo 1 Bordas, Stéphane Pierre Alain 1 Broggi, Alberto 1 Brubeck, Pablo D. 1 Bulle, Raphaël 1 Chan, Jesse 1 Chiang, Wen-Chyuan 1 Chouly, Franz 1 Conte, Gianni 1 Cullen, Michael John Priestley 1 Dubos, Thomas 1 Eldred, Christopher 1 Espath, Luis F. R. 1 Farrell, Patrick E. 1 Farrell, Patrick Emmet 1 Fascioli, Alessandra 1 Funke, Simon W. 1 Gorman, Gerard J. 1 Han, Danfu 1 Heath, Michael T. 1 Hiester, H. R. 1 Homolya, Miklós 1 Hu, Xianliang 1 Jahn, Mischa 1 Kincl, Ondřej 1 Kouvelis, Panagiotis 1 Kritsikis, Evaggelos 1 Lin, Guang 1 Lozinski, Alexei 1 Maddison, James R. 1 Marchena-Menéndez, Jorge 1 Mardal, Kent-Andre 1 Markall, Graham R. 1 Marsik, Frantisek 1 Mclean Wolf, Michael 1 Milz, Johannes 1 Montalvo Urquizo, Jonathan 1 Müller, Eike Hermann 1 Pavelka, Michal 1 Pena, Gonçalo 1 Prud’homme, Christophe 1 Pusztay, Joseph V. 1 Ramani, Karthik 1 Rathgeber, Florian 1 Rosales, Rodolfo Ruben 1 Ruggeri, Fabrizio 1 Russell, Francis P. 1 Sedláček, Miroslav 1 Seibold, Benjamin 1 Shao, Xinping 1 Shipton, Jemma 1 Shirokoff, David 1 Terrel, Andy R. 1 Theisen, Lambert 1 Torrilhon, Manuel 1 Ulbrich, Michael 1 van Bloemen Waanders, Bart G. 1 Vidakovic, Brani 1 Warburton, Timothy 1 Wechsung, Florian 1 Wells, Garth N. 1 Winovich, Nick 1 Yamazaki, Hiroe 1 Zhou, Dong all top 5 Cited in 13 Serials 14 SIAM Journal on Scientific Computing 9 ACM Transactions on Mathematical Software 5 Journal of Computational Physics 4 Computers & Mathematics with Applications 3 Computer Methods in Applied Mechanics and Engineering 2 Applied Mathematical Modelling 1 BIT 1 Journal of Computational and Applied Mathematics 1 Journal of Statistical Planning and Inference 1 SIAM Journal on Control and Optimization 1 Annals of Operations Research 1 SIAM Journal on Applied Mathematics 1 Archives of Computational Methods in Engineering all top 5 Cited in 16 Fields 34 Numerical analysis (65-XX) 12 Partial differential equations (35-XX) 10 Fluid mechanics (76-XX) 8 Mechanics of deformable solids (74-XX) 7 Computer science (68-XX) 3 Geophysics (86-XX) 3 Operations research, mathematical programming (90-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Biology and other natural sciences (92-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Systems theory; control (93-XX) Citations by Year