Parallel domain-decomposition preconditioning for computational fluid dynamics

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

Volumn 1573, Issue , 1999, Pages 176-202

  Barth, Timothy J ^a   Chan, Tony F ^b   Tang, Wei Pai ^c  

^a NASA AMES RESEARCH CENTER   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84869095152     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/10703040_15     Document Type: Conference Paper

References (29)

1. T. J. Barth, Parallel CFD algorithms on unstructured meshes, Tech. Report AGARD R-907, Advisory Group for Aerospace Research and Development, 1995.
2. T. J. Barth, T. F. Chan, and W.-P. Tang, A parallel non-overlapping domain-decomposition algorithm for compressible fluid flow problems on triangulated domains, AMS Cont. Math. 218 (1998).
3. T.J. Barth, Numerical methods for gas-dynamic systems on unstructured meshes, An Introduction to Recent Developments in Theory and Numerics for Conservation Laws (Kröner, Ohlberger and Rohde eds.), Lecture Notes in Computational Science and Engineering, vol. 5, Springer-Verlag, Heidelberg, 1998, pp. 195-285.
4. P. Bjorstad and O. B. Widlund, Solving elliptic problems on regions partitioned into substructures, SIAM J. Numer. Anal. 23 (1986), no. 6, 1093-1120.
5. J. H. Bramble, J. E. Pasciak, and A. H. Schatz, The construction of preconditioners for elliptic problems by substructuring, I, Math. Comp. 47 (1986), no. 6, 103-134.
6. J. H. Bramble, J. E. Pasciak, and J. Xu, The analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems, Math. Comp. 51 (1988), 289-414.
7. A. Brandt and I. Yavneh, Accelerated multigrid convergence for high-Reynolds recirculating flow, SIAM J. Sci. Comp. 14 (1993), 607-626.
8. T. Chan and J. Zou, Additive Schwarz domain decomposition methods for elliptic problems on unstructured meshes, Tech. Report CAM 93-40, UCLA Department of Mathematics, December 1993.
9. T. F. Chan and T. Mathew, Domain decomposition algorithms, Acta Numerica (1994), 61-143.
10. D. F. D’Azevedo, P. A. Forsyth, and W.-P. Tang, Toward a cost effective ilu preconditioner with high level fill, BIT 32 (1992), 442-463.
11. M. Dryja, B. F. Smith, and O. B. Widlund, Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions, SIAM J. Numer. Anal. 31 (1994), 1662-1694.
12. M. Dryja and O.B. Widlund, Some domain decomposition algorithms for elliptic problems, Iterative Methods for Large Linear Systems (L. Hayes and D. Kincaid, eds.), 1989, pp. 273-291.
13. M. Dryja and O.B. Widlund, Additive Schwarz methods for elliptic finite element problems in three dimensions, Fifth Conference on Domain Decomposition Methods for Partial Diffierential Equations (T. F. Chan, D.E. Keyes, G.A. Meurant, J.S. Scroggs, and R.G. Voit, eds.), 1992.
14. T. Dupont, R. Kendall, and H. Rachford, An approximate factorization procedure for solving self-adjoint elliptic diffierence equations, SIAM J. Numer. Anal. 5 (1968), 558-573.
15. D. J. Evans, The use of pre-conditioning in iterative methods for solving linear equations with symmetric positive definite matrices, J. Inst. Maths. Appl. 4 (1968), 295-314.
16. G. Golub and D. Mayers, The use of preconditioning over irregular regions, Comput. Meth. Appl. Mech. Engrg. 6 (1984), 223-234.
17. T. J. R. Hughes, L. P. Franca, and M. Mallet, A new finite element formulation for CFD: I. symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Comp. Meth. Appl. Mech. Engrg. 54 (1986), 223-234.
18. T. J. R. Hughes and M. Mallet, A new finite element formulation for CFD: III. the generalized streamline operator for multidimensional advective-diffusive systems, Comp. Meth. Appl. Mech. Engrg. 58 (1986), 305-328.
19. G. Karypis and V. Kumar, Multilevel k-way partitioning scheme for irregular graphs, Tech. Report 95-064, U. of Minn. Computer Science Department, 1995.
20. D. J. Mavriplis, A three dimensional multigrid Reynolds-averaged Navier-Stokes solver for unstructured meshes, Tech. Report 94-29, ICASE, NASA Langley R.C., 1994.
21. J. A. Meijerink and H. A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comp. 34 (1977), 148-162.
22. J. S. Przemieniecki, Matrix structural analysis of substructures, Am. Inst. Aero. Astro. J. 1 (1963), 138-147.
23. Y. Saad, A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Stat. Comp. 14 (1993), no. 2, 461-469.
24. H. A. Schwarz, Uber einige abbildungensaufgaben, J. Reine Angew. Math. 70 (1869), 105-120.
25. V. Simoncini and E. Gallopoulos, An iterative method for nonsymmetric systems with multiple right-hand sides, SIAMJ. Sci. Comp. 16 (1995), no. 4, 917-933.
26. B. Smith, P. Bjorstad, and W. Gropp, Domain decomposition: parallel multilevel methods for elliptic partial differential equations, Cambridge University Press, 1996.
27. H. Stone, Iterative solution of implicit approximations of multidimensional partial differential equations, SIAM J. Numer. Anal. 5 (1968), 530-558.
28. Y. Wu, X.-C. Cai, and D. E. Keyes, Additive Schwarz methods for hyperbolic equations, AMS Cont. Math. 218 (1998).
29. J. Xu, An introduction to multilevel methods, Lecture notes: VIIth EPSRC numerical analysis summer school, 1997.