Diagonal-implicitly iterated Runge-Kutta methods on distributed memory machines

International Journal of High Speed Computing

Volumn 10, Issue 2, 1999, Pages 185-207

  Rauber, Thomas ^a   Rünger, Gudula ^b  

^a MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0003495443     PISSN: 01290533     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129053399000090     Document Type: Article

References (32)

1. T. Agerwal, J. L. Martin, J. H. Mirza, D. C. Sadler, D. M. Dias, and M. Snir, "SP2 System Architecture", IBM System J. 34(2), 152-184 (1995).
2. G. S. Almasi and A. Gottlieb, Highly Parallel Computing (Benjamin/Cummings, 1994).
3. C. B. Stunkel an D. G. Shea, B. Abadi, M. G. Bender, D. G. Grice, P. Hochschild, D. J. Joseph, B. J. Nathanson, R. A. Swetz, R. F. Stucke, M. Tsao, and P. R. Varker, "The SP2 High-Performance Switch", IBM System J. 34(2), 185-204 (1995).
4. K. Burrage, "Parallel methods for initial value problems", Applied Numerical Mathematics 11, 5-25 (1993).
5. K. Burrage, Parallel and Sequential Methods for Ordinary Differential Equations (Oxford Science Publications, 1995).
6. K. Burrage and S. Plowman, "The numerical solution of ODEIVPs in a transputer environment", Applications of Tranputers 2, 495-505 (1990).
7. P. Deuflhard, "Recent progress in extrapolation methods for ordinary differential equations", SIAM Review 27, 505-535 (1985).
8. The MPI Forum, "MPI: A Message Passing Interface Standard", Technical report, University of Tennessee, April 1994.
9. C. W. Gear, "Massive Parallelism across Space in ODEs", Applied Numerical Mathematics 11, 27-43 (1993).
10. C. W. Gear and Xu Hai, "Parallelism in Time for ODEs", Applied Numerical Mathematics 11, 45-68 (1993).
11. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer-Verlag, Berlin, 1993).
12. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II (Springer, 1991).
13. A. Iserles and S. P. Nørsett, "On the Theory of Parallel Runge-Kutta Methods", IMA Journal of Numerical Analysis 10, 463-488 (1990).
14. B. M. S. Khalaf and D. Hutchinson, "Parallel Algorithms for Initial Value Problems: Parallel Shooting," Parallel Computing 18, 661-673 (1992).
15. M. Kiehl, "Simulation of Multibody Systems by a Parallel Extrapolation Method", Technical Report TUM-M9303, Technische Universität München, January 1993.
16. R. Lefever and G. Nicolis, "Chemical Instabilities and Sustained Oscillations", J. Theor. Biol. 30, 267-284 (1971).
17. W. Liniger and R. A. Willoughby, "Eficient Integration Methods for Stiff Systems of Ordinary Differential Equations", SIAM Journal of Applied Analysis 7, 47-66 (1970).
18. L. Lustman, B. Neta, and W. Gragg, "Solution of ordinary differential initial value problems on an Intel Hypercube", Computer Math. Applications 23(10), 65-72 (1992).
19. S. P. Nørsett and H. H. Simonsen, "Aspects of Parallel Runge-Kutta methods", in Numerical Methods for Ordinary Differential Equations, Lecture Notes in Mathematics, vol. 1386, 1989, pp. 103-117.
20. K. Potma and W. Hoffmann, "Boosting the Performance of the Linear Algebra part in an ODE solver for shared Memory Systems", Future Generation Computer Systems 10(2), 315-319 (1994).
21. T. Rauber and G. Rünger, "Parallel Solution of a Schrödinger-Poisson system", in International Conference on High-Performance Computing and Networking Springer LNCS 919, 1995, pp. 697-702.
22. T. Rauber and G. Rünger, "Comparing Task and Data Parallel Execution Schemes for the DIIRK method", in Proc. EuroPar'96, Springer LNCS 1124, 1996, pp. 52-61.
23. T. Rauber and G. Rünger, "Parallel Iterated Runge-Kutta Methods and Applications̈, International Journal of Supercomputer Applications 10(1), 62-90 (1996).
24. T. Rauber and G. Rünger, "Load Balancing Schemes for Extrapolation Methods", Concurrency: Practice and Experience 9(3), 181-202 (1997).
25. L. F. Shampine, H. A. Watts, and S. M. Davenport, "Solving Nonstiff Ordinary Differential Equations - the State of the Art", SIAM Review 18(3), 376-411 (1976).
26. M. Snir, P. Hochschild, D. D. Frye, and K. J. Gildea, "The communication software and parallel environment of the IBM SP2", IBM System J. 34(2), 205-221 (1995).
27. H. W. Tam, "One-Stage Parallel Methods for the Numerical Solution of Ordinary Differential Equation", SIAM Journal on Scientific and Statistical Computing 13(5), 1039-1061 (1992).
28. P. J. van der Houwen and B. P. Sommeijer, "Parallel Iteration of high-order Runge-Kutta Methods with stepsize control", Journal of Computational and Applied Mathematics 29, 111-127 (1990).
29. P. J. van der Houwen and B. P. Sommeijer, "Iterated Runge-Kutta Methods on Parallel Computers", SIAM Journal on Scientific and Statistical Computing 12(5), 1000-1028 (1991).
30. P. J. van der Houwen and B. P. Sommeijer, "The Use of Approximate Factorization in Stiff ODE solvers", Technical Report MAS-R9732, CWI, November 1997.
31. P. J. van der Houwen, B. P. Sommeijer, and W. Couzy, "Embedded Diagonally Implicit Runge-Kutta Algorithms on Parallel Computers", Mathematics of Computation 58(197), 135-159 (1992).
32. J. K. White and A. Sangiovanni-Vincentelli, Relaxation Techniques for the Simulation of VLSI Circuits (Kluwer Academic Publisher, 1987).