Optimizing the evaluation of finite element matrices

SIAM Journal on Scientific Computing

Volumn 27, Issue 3, 2006, Pages 741-758

  Kirby, Robert C ^a   Knepley, Matthew ^b   Logg, Anders ^c   Scott, L Ridgway ^d  

^a THE UNIVERSITY OF CHICAGO   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

^c TOYOTA TECHNOLOGICAL INSTITUTE AT CHICAGO   (United States)

^d UNIVERSITY OF CHICAGO   (United States)

Author keywords

Compiler; Finite element; Variational form

Indexed keywords

COMPUTATION THEORY; GRAPH THEORY; HEURISTIC METHODS; LAPLACE TRANSFORMS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS; OPTIMIZATION;

FINITE ELEMENT COMPUTATIONS; HEURISTIC GRAPH ALGORITHMS; NAVIER-STOKES OPERATORS; STIFFNESS MATRICES;

FINITE ELEMENT METHOD;

EID: 33646556105     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/040607824     Document Type: Article

References (27)

1. A. A. ALBRECHT, F. GOTTSCHLING. AND U. NAUMANN, Markowitz-type heuristics for computing Jacobian matrices efficiently, in International Conference on Computational Science, Part II, Lecture Notes in Comput. Sci. 265 Springer, Berlin, 2003, pp. 575-584.
2. D. N. ARNOLD, D. BOFFI, AND R. S. FALK, Quadrilateral H(div) finite elements. SLAM J. Numer. Anal., 42 (2005), pp. 2429-2491.
3. S. BALAY, K. BUSCHELMAN, V. EIJKHOUT, W. D. GROPP, D. KAUSHIK, M. G. KNEPLEY, L. C. MCINNES, B. F. SMITH, AND H. ZHANG, PETSc Users Manual, Tech. Report ANL-95/11, Revision 2.1.5, Argonne National Laboratory, Argonne, IL, 2004.
4. S. C. BRENNER AND L. R. SCOTT, The Mathematical Theory of Finite Element Methods, 2nd ed., Springer-Verlag, New York, 2002.
5. K. A. CLIFFE AND S. J. TAVENER, Implementation of extended systems using symbolic algebra, in Continuation Methods in Fluid Dynamics, D. Henry and A. Bergeon, eds., Notes Numer. Fluid Mech. 74, Vieweg, Braunschweig, 2000, pp. 81-92.
6. M. CROUZEIX AND P.-A. RAVIART, Conforming and nonconforming finite element methods for solving the stationary Stokes equations. I, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge, 7 (1973), pp. 33-75.
7. J. A. GUNNELS, F. G. GUSTAVSON, G. M. HENRY. AND R. A. VAN DE GEIJN, FLAME: Formal linear algebra methods environment, Trans. Math. Software, 27 (2001), pp. 422-455.
8. P. HANSBO AND A. SZEPESSY, A velocity-pressure streamline diffusion finite element method for the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 84 (1990), pp. 175-192.
9. V. HENSON AND U. YANG, BoomerAMG: A parallel algebraic multigrid solver and preconditioner, Appl. Numer. Math., 41 (2002), pp. 155-177.
10. J. HOFFMAN AND U. YANG, DOLFIN: Dynamic Object Oriented Library for Finite Element Computation, Tech. Report 2002-6, Chalmers Finite Element Preprint Series, Chalmers University, Göteborg, Sweden, 2002, http://www.fenics.org/dolfin.
11. T. J. R. HUGHES, L. P. FRANCA, AND M. BALESTRA, A new finite element formulation for computational fluid dynamics. V. Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations, Comput. Methods Appl. Mech. Engrg., 59 (1986), pp. 85-99.
12. E.-J. IM AND K. A. YELICK, Optimizing sparse matrix computations for register reuse in SPARSITY, in Proceedings of the International Conference on Computational Science, (San Francisco, CA), Lecture Notes in Comput. Sci. 2073, Springer, New York, 2001, pp. 127-136.
13. E.-J. IM, K. A. YELICK, AND R. VUDUC, SPARSITY: Framework for optimizing sparse matrix-vector multiply, Int. J. High Performance Comput. Appl., 18 (2004), pp. 135-158.
14. H. JUAREZ, L. R. SCOTT, R. METCALFE, AND B. BAGHERI, Direct simulation of freely rotating cylinders in viscous flows by high-order finite element methods, Comput. & Fluids, 29 (2000), pp. 547-582.
15. R. C. KIRBY, Algorithm 839: FIAT, a new paradigm for computing finite element basis functions, ACM Trans. Math. Software, 30 (2004), pp. 502-516.
16. R. C. KIRBY, M. KNEPLEY, AND L. SCOTT, Evaluation of the Action of Finite Element Operators, Tech. report TR-2004-07, Department of Computer Science, University of Chicago, Chicago, IL, 2004.
17. D. E. KNUTH, The Art of Computer Programming, Volume 2: Seminumerical Algorithms, 3rd ed., Addison-Wesley, Reading, MA, 1997.
18. ARGONNE NATIONAL LABORATORY, PETSc-CS Alphan, http://www-unix.mcs.anl. gov/petsc/petsc-3/.
19. A. LOGG, FFC: The FEniCS Form Compiler, http://www.fenics.org/ffc.
20. K. LONG, Sundance rapid prototyping tool for parallel PDE optimization, in Large-Scale PDE-Constrained Optimization, Lecture Notes in Comput. Sci. Engrg. 30, Springer, Berlin, 2003, pp. 331-341.
21. K. LONG, Sundance, 2003, http://csmr.ca.sandia.gov/~krlong/sundance.html.
22. R. VUDUC, J. DEMMEL, AND J. BILMES, Statistical models for empirical search-based performance tuning, Int. J. High Performance Comput. Appl., 18 (2004), pp. 65-94.
23. R. VUDUC, J. W. DEMMEL, K. A. YELICK, S. KAMIL, R. NISHTALA, AND B. LEE, Performance optimizations and bounds for sparse matrix-vector multiply, in Proceedings of Supercomputing. Baltimore, MD, IEEE, Piscataway, NJ, 2002, pp. 1-35.
24. TAx, in Proceedings of the ICCS Workshop on Parallel Linear Algebra, P. M. A. Sloot, D. Abramson, A. V. Bogdanov, J. J. Dongarra, A. Y. Zomaya, and Y. E. Gorbachev, eds., (Melbourne, Australia), Lecture Notes in Comput. Sci. 2660, Springer, New York, 2003, pp. 705-714.
25. R. VUDUC, S. KAMIL, J. Hsu, R. NISHTALA, J. W. DEMMEL, AND K. A. YELICK, Automatic performance tuning and analysis of sparse triangular solve, presented at the Workshop on Performance Optimization via High-Level Languages and Libraries, in conjunction with the 16th International Conference on Supercomputing (ICS), ACM, New York, 2002. Available online at http://www.cs.berkeley.edu/~richie/research/pubs.html
26. R. C. WHALEY, A. PETITET, AND J. J. DONGARRA, Automated empirical optimization of software and the ATLAS project, Parallel Computing, 27 (2001), pp. 3-35.
27. Also available online as University of Tennessee LAPACK Working Note 147, UT-CS-00-448 at www.netlib.org/lapack/lawns/downloads.