A parallel adaptive coupling algorithm for systems of differential equations

Journal of Computational Physics

Volumn 161, Issue 2, 2000, Pages 401-427

  Garbey, M ^a   Tromeur Dervout, D ^a  

^a UNIVERSITÉ LYON 1   (France)

Author keywords

Algorithms for specific classes of architectures; Combustion; Complexity and performance of numerical algorithms; Discrete Fourier transforms; Extrapolation methods; Parallel computation; Stability and convergence of numerical methods

Indexed keywords

APPROXIMATION ALGORITHMS; CODES (SYMBOLS); COMBUSTION; COMPLEX NETWORKS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS;

ALGORITHM FOR SPECIFIC CLASS OF ARCHITECTURE; COMPLEXITY AND PERFORMANCE OF NUMERICAL ALGORITHM; EXTRAPOLATION METHODS; META-COMPUTING; NUMERICAL ALGORITHMS; PARALLEL COMPUTATION; PARALLEL COMPUTER; PERFORMANCE; SPECIFIC CLASS; STABILITY AND CONVERGENCE OF NUMERICAL METHODS;

DISCRETE FOURIER TRANSFORMS;

EID: 0006703138     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.2000.6500     Document Type: Article

References (25)

1. D. P. Bertsekas and J. N. Tsitsiklis, Parallel and Distributed Computation, Numerical Methods (Prentice-Hall, Englewood Cliffs, NJ, 1989).
2. G. Bowden et al., Effect of convection on a propagating front with a solid product: Comparison of theory and experiments, J. Phy. Chem. B 101, No. 4, 678 (1997).
3. M. Crouzeix and A. L. Mignot, Analyse Numérique des équations différentielles (Masson, 1983).
4. J. Dongarra, Solving computational grand challenges using a network of heterogeneous supercomputers, in Proceedings, Fifth SIAM Conference on Parallel Processing for Scientific Computing (1991), pp. 596-601.
5. A. Ecer, N. Gopalaswamy, H. U. Akay, and Y. P. Chien, Digital filtering techniques for parallel computation of explicit schemes, AIAA Paper 98-0616.
6. G. Edjlali, M. Garbey, and D. Tromeur-Dervout, Interoperability parallel programs approach to simulate 3D frontal polymerization process, J. Parallel Comput. 25, 1161 (1999).
7. G. E. Fagg, K. Moore, J. Dongarra, and A. Geist, Scalable networked information processing environment (SNIPE), in Proceedings, Super Computing 97 (Comput. Soc. Press, New York, 1997).
8. I. Foster and C. Kesselman, Globus: A metacomputing infrastructure toolkit, Int. J. Supercomput. Appl. 11, No. 2, 115 (1997).
9. M. Garbey, A. Taik, and V. Volpert, Linear stability analysis of reaction fronts in liquids, Q. Appl. Math. 54, No. 2, 225 (1996).
10. M. Garbey and D. Tromeur-Dervout, Massively parallel computation of stiff propagating combustion front, IOP J. Comb. Theory Model. 3, No. 1, 271 (1997).
11. M. Garbey and D. Tromeur-Dervout, A new parallel solver for non periodic incompressible Navier-Stokes equations with Fourier basis: Application to frontal polymerisation, J. Comput. Phys. 145, No. 1, 316 (1998).
12. M. Garbey and D. Tromeur-Dervout, Application of local Fourier basis to domain decomposition in combustion problems, in Proceedings, Inter. Conf. Parallel CFD98, edited by C. A. Lin et al. (1998), pp. 199-204.
13. M. Garbey and D. Tromeur-Dervout, Domain decomposition with local Fourier bases applied to frontal polymerization problems, in Proceedings, Inter. Conf. DD11, edited by Ch.-H. Lai et al. (1998), pp. 242-250.
14. M. Garbey and D. Tromeur-Dervout, Level domain decomposition for multiclusters, in Proceedings, Inter. Conf. DD12, edited by T. Chan et al. (Chiba, 1999).
15. M. Garbey, On some applications of the superposition principle with Fourier basis, CDCSP preprint 97-03. [To appear in SIAM Sci. Comput.]
16. D. Gottlieb and C.W. Shu, On the Gibbs phenomenon and its resolution, SIAM Rev. 39, No. 4, 644 (1998).
17. W. Gropp, E. Lusk, and A. Skjellum, Using MPI, Scientific and Engineering Computation Series (MIT Press, Cambridge, MA, 1994).
18. P. Gray and S. K. Scott, Chemical Oscillations and Instabilities, The International Series of Monographs on Chemistry, Vol. 21 (Clarendon Press, Oxford, 1990).
19. J. D. Murray, Mathematical Biology, Biomathematics Texts, 2nd ed., Vol. 19 (Springer-Verlag, Berlin/New York, 1993).
20. M. Israeli, L. Vozovoi, and A. Averbuch, Spectral multidomain technique with local Fourier basis, J. Sci. Comput. 8, No. 2, 135 (1993).
21. M. Israeli, L. Vozovoi, and A. Averbuch, Domain decomposition methods for solving parabolic PDEs on multiprocessors, Appl. Numer. Math. 12, Nos. 1-3, 193 (1993); Domain decomposition methods with local Fourier basis for parabolic problems, Contemp. Math., 157 (1994).
22. M. Israeli, L. Vozovoi, and A. Averbuch, Domain decomposition methods for solving parabolic PDEs on multiprocessors, Appl. Numer. Math. 12, Nos. 1-3, 193 (1993); Domain decomposition methods with local Fourier basis for parabolic problems, Contemp. Math., 157 (1994).
23. M. Israeli, L. Vozovoi, and A. Averbuch, Spectral multidomain technique with local Fourier basis, J. Sci. Comput. 9, No. 3, 311 (1994).
24. D. Patterson and J. L. Hennessy, Computer Architecture: A Quantitative Approach (Morgan Kaufman, San Mateo, CA, 1990).
25. J. Pojman, R. Graven, A. Khan, and W. West, Convective instabilities in traveling fronts of addition polymerization, J. Phys. Chem. 96, 7466 (1992).