Online checkpointing for parallel adjoint computation in PDEs: Application to goal-oriented adaptivity and flow control

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4128 LNCS, Issue , 2006, Pages 689-699

  Heuveline, Vincent ^a   Walther, Andrea ^b  

^a UNIVERSITY OF KARLSRUHE   (Germany)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL FLUID DYNAMICS; DIFFERENTIAL EQUATIONS; ERROR DETECTION; PROBLEM SOLVING;

ERROR CONTROL; OFFLINE CHECKPOINTING; PARALLEL ADJOINT COMPUTATION;

ONLINE SYSTEMS;

EID: 33750027996     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11823285_72     Document Type: Conference Paper

References (20)

1. S.C. Brenner and R.L. Scott. The mathematical theory of finite element methods. Springer, Berlin-Heidelberg-New-York, 1994.
2. F. Brezzi and R. Falk. Stability of higher-order Hood-Taylor methods. SIAM J. Numer. Anal., 28(3):581-590, 1991.
3. K. Eriksson, D. Estep, P. Hansbo, and C. Johnson. Introduction to adaptive methods for differential equations. Ada Numerica, 4:105-158, 1995.
4. K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems, I: A linear model problem. SIAM J. Numer. Anal, 28:43-77, 1991.
5. K. Eriksson and C. Johnson. Adaptive finite element methods for parabolic problems, II, IV, V. SIAM J. Numer. Anal., 32:706-740,
6. K. Eriksson and C. Johnson. SIAM J. Numer. Anal. 32:1729-1763, 1995.
7. M.B. Giles. On adjoint equations for error analysis and optimal grid adaptation. In D.A. Caughey and M.M. Hafez, editors, In Frontiers of Computational Fluid Dynamics 1998, pages 155-170. World Scientific, 1998.
8. A. Griewank and A. Walther. Revolve: An implementation of checkpointing for the reverse or adjoint mode of computational differentiation. ACM Trans. Math. Software, 26:19-45, 2000.
9. M.D. Gunzburger. Perspectives in flow control and optimization. Advances in Design and Control 5. Philadelphia, SIAM., 2003.
10. V. Heuveline. On higher-order mixed FEM for low Mach number flows: Application to a natural convection benchmark problem. Int. J. Num. Meth. Fluids, 41(12):1339-1356, 2003.
11. V. Heuveline and A. Walther. Towards the economical computation of adjoints in PDEs using optimal online checkpointing. In preparation, 2006.
12. M. Hinze and J. Sternberg. A-revolve: An adaptive memory- and run-time-reduced procedure for calculating adjoints; with an application to the instationary Navier-Stokes system. Opti. Meth. Softw., 20:645-663, 2005.
13. P. Hood and C. Taylor. A numerical solution of the Navier-Stokes equations using the finite element techniques. Comp. and Fluids, 1:73-100, 1973.
14. L. Machiels, A.T. Patera, and J. Peraire. Output bound approximation for partial differential equations; application to the incompressible Navier-Stokes equations. In S. Biringen, editor, Industrial and Environmental Applications of Direct and Large Eddy Numerical Simulation. Springer, 1998.
15. J.T. Oden and S. Prudhomme. On goal-oriented error estimation for elliptic problems: Application to the control of pointwise errors. Comput. Methods Appl. Mech. Eng., 176:313-331, 1999.
16. Y. Saad. Iterative methods for sparse linear systems. Computer Science/Numerical Methods. PWS Publishing Company, 1996.
17. M. Schafer and S. Turek. Benchmark computations of laminar flow around cylinder. Notes on numerical fluid mechanics, 52:856-869, 1996.
18. R. Serban and A.C. Hindmarsh. CVODES: An ODE solver with sensitivity analysis capabilities. UCRL-JP-20039, LLNL, 2003.
19. A. Walther and A. Griewank. Advantages of binomial checkpointing for memory-reduced adjoint calculations. In M. Feistauer et al., editor, Numerical mathematics and advanced applications, pages 834-843. Springer, 2004.
20. P. Wesseling. An introduction to multigrid methods. Wiley, Chichester, 1992.