Unified framework for finite element assembly

International Journal of Computational Science and Engineering

Volumn 4, Issue 4, 2009, Pages 231-244

  Alnæs, Martin Sandve ^a   Logg, Anders ^b   Mardal, Kent Andre ^b   Skavhaug, Ola ^b   Langtangen, Hans Petter ^b  

^a SIMULA RESEARCH LABORATORY   (Norway)

^b UNIVERSITY OF OSLO   (Norway)

Author keywords

Assembly; Code generation; Finite elements; Implementation; UFC; Unified form assembly code

Indexed keywords

ASSEMBLY; CODES (SYMBOLS); GALERKIN METHODS; LINEAR ALGEBRA;

ASSEMBLY CODE; CODE GENERATION; DISCONTINUOUS GALERKIN METHODS; FINITE ELEMENT PROBLEMS; FINITE ELEMENT PROGRAMS; FINITE ELEMENT SIMULATIONS; IMPLEMENTATION; MIXED FINITE ELEMENTS;

FINITE ELEMENT METHOD;

EID: 70749109887     PISSN: 17427185     EISSN: 17427193     Source Type: Journal    
DOI: 10.1504/IJCSE.2009.029160     Document Type: Article

References (27)

1. Alnæs, M., Langtangen, H-P., Logg, A., Mardal, K-A. and Skavhaug, O. (2008) UFC Specification and User Manual, http://www.fenics.org/ufc/
2. Alnæs, M.S. and Mardal, K-A. (2008) SyFi: Symbolic Finite Elements http://www.fenics.org/syfi/
3. Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F. and Zhang, H. (2008) PETSc, http://www.mcs.anl.gov/petsc/
4. Bangerth, W., Hartmann, R. and Kanschat, G. (2006) Deal. II Differential Equations Analysis Library, http://www.dealii.org/
5. Bangerth, W., Hartmann, R. and Kanschat, G. (2007) 'Deal. II - a general-purpose object-oriented finite element library', ACM Trans. Math. Softw., Vol. 33, No. 4, Article no. 24.
6. Bastian, P., Birken, K., Lang, S., Johannsen, K., Neuss, N., Rentz-Reichert, H. and Wieners, C. (1997) 'UG - a flexible software toolbox for solving partial differential equations', Computing and Visualization in Science, Vol. 1, pp.27-40.
7. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M. and Sander, O. (2008a) 'A generic grid interface for parallel and adaptive scientific computing. Part I: Abstract framework', Computing, Vol. 82, No. 2, July, pp.103-119, http://dx.doi.org/ 10.1007/s00607-008-0003-x
8. Bastian, P., Blatt, M., Dedner, A., Engwer, C., Klöfkorn, R., Ohlberger, M. and Sander, O. (2008b) 'A generic grid interface for parallel and adaptive scientific computing. Part II: Implementation and tests in DUNE', Computing, Vol. 82, No. 2, July, pp.121-138, http://dx.doi.org/10.1007/s00607-008-0004-9
9. Bauer, C., Dams, C., Frink, A., Kisil, V.V., Kreckel, R., Sheplyakov, A. and Vollinga, J. (2006) GiNaC, http://www.ginac.de
10. Ciarlet, P.G. (1978) The Finite Element Method for Elliptic Problems North-Holland, Amsterdam, New York, Oxford.
11. Hughes, T.J.R. (1987) The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
12. Knepley, M.G. and Karpeev, D.A. (2009) 'Mesh algorithms for PDE with Sieve I: Mesh distribution', Scientific Programming, To appear, http://www.mcs.anl.gov/uploads/cels/papers/P1455.pdf
13. Kirby, R.C. and Logg, A. (2006) 'A compiler for variational forms', ACM Transactions on Mathematical Software, Vol. 32, No. 3, pp.417-444.
14. Kirby, R.C. and Logg, A. (2007) 'Efficient compilation of a class of variational forms', ACM Transactions on Mathematical Software, Vol. 33, No. 3, Article no. 17.
15. Kirby, R.C. (2004) 'FIAT: A new paradigm for computing finite element basis functions', ACM Trans. Math. Software, Vol. 30, pp.502-516.
16. Langtangen, H.P. (2003a) Computational Partial Differential Equations - Numerical Methods and Diffpack Programming, 2nd ed., Texts in Computational Science and Engineering, Vol. 1, Springer, http://www.diffpack.com
17. Langtangen, H.P. (2003b) Computational Partial Differential Equations - Numerical Methods and Diffpack Programming, 2nd ed., Springer-Verlag, Berlin, p.855.
18. Logg, A., Oelgaard, K., Rognes, M. and Wells, G.N. (2008) FFC: FEniCS Form Compiler, http//www.fenics.org/ffc/
19. Logg, A. and Wells, G.N. (2009) DOLFIN: Automated Finite Element Computing, Submitted, http://www.fenics.org/pub/documents/dolfin/ papers/dolfin-2009.pdf
20. Logg, A. (2007) 'Automating the finite element method', Arch. Comput. Methods Eng., Vol. 14, No. 2, pp.93-138.
21. Logg, A. (2009) 'Efficient representation of computational meshes', Submitted to International Journal of Computational Science and Engineering, Vol. 4, No. 4, pp.283-295.
22. Long, K. (2006) Sundance, http://software.sandia.gov/sundance/
23. Meerbergen, K. (2008) GLAS: Generic Interface for Linear Algebra Software, http://glas.sourceforge.net/
24. Ring, J., Langtangen, H.P. and Bredesen, R. (2008) 'Easyviz', Subpackage of SciTools, http://code.google.com/p/scitools/
25. Skavhaug, O., Alnæs, M.S., Mardal, K-A., Staff, G. and Ødegård, Å. (2008) 'PyCC', Software Framework Under Development, http://www.simula.no/pycc
26. Thuné, M., Mossberg, E., Olsson, P., Rantakokko, J., Åhlander, K. and Otto, K. (1997) 'Object-oriented construction of parallel PDE solvers', in Arge, E., Bruaset, A.M. and Langtangen, H.P. (Eds.): Modern Software Tools for Scientific Computing, Birkhäuser, pp.203-226.
27. Zienkiewicz, O.C., Taylor, R.L. and Zhu, J.Z. (1967-2005) The Finite Element Method - Its Basis and Fundamentals, 6th ed., Elsevier, Oxford.