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Domain decomposition methods for the parallel computation of reacting flows. (English) Zbl 0804.76066

We make comparisons between relaxation-based linear solvers and also preconditioned iterative methods of conjugate gradient and Chebyshev type, focusing attention on both iteration count and global inner product count. The generalized minimum residual method with block-ILU preconditioning is judged the best serial method among those considered, and parallel numerical experiments on the Encore Multimax demonstrate for it approximately ten-fold speedup on 16 processors.

MSC:

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76V05 Reaction effects in flows
76M20 Finite difference methods applied to problems in fluid mechanics
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65Y05 Parallel numerical computation

References:

[1] Ashby, S. F., (Technical Report UIUCDCS-R-85-1203 (May 1985), Dept. of Computer Science, University of Illinois)
[2] Ashcraft, C.; Grimes, R., (Technical Report ETA-TR-41 (December 1986), Boeing Computer Services)
[3] Ashcraft, C., (Technical Report ETA-TR-49 (April 1987), Boeing Computer Services)
[4] Bank, R. E.; Coughran, W. M.; Driscoll, M. A.; Smith, R. K.; Fichtnes, W., Comput. Phys. Commun., 53, 201 (1989)
[5] D.J. Baxter, personal communication (1987).; D.J. Baxter, personal communication (1987).
[6] Bramble, J. H.; Pasciak, J. E.; Schatz, A. HG., Math. Comput., 47, 103 (1986) · Zbl 0615.65112
[7] Chan, T. F.; Glowinski, R.; Periaux, J.; Widlund, O., (Second Intern. Symp. on Domain Decomposition Methods (1989), SIAM: SIAM Philadelphia), to appear
[8] Chan, T. F.; Goovaerts, D., ((June 1988), UCLA Comp. and App. Math)
[9] (Proc. IV Coloq. de Matemáticas del CINVESTAV. Proc. IV Coloq. de Matemáticas del CINVESTAV, Worshop in Numerical Analysis and its applications (18-24 August 1985)), Taxco, Mexico
[10] Cottle, R. W., Lin. Alg. Appl., 8, 189 (1974) · Zbl 0284.15005
[11] Curtis, A. R.; Powell, M. J.; Reid, J. K., J. Inst. Math. Appl., 13, 117 (1974) · Zbl 0273.65036
[12] Dryja, M.; Widlund, O. B., (Technical Report 339 (December 1987), Courant Institute of Mathematical Sciences, NYU)
[13] Elman, H. C.; Saad, Y.; Saylor, P. E., (Technical Report 301 (February 1984), Dept. of Computer Science, Yale University)
[14] Giovangigli, V.; Darabiha, N., Vector Computers and Complex Chemistry Combustion, (Brauner, C. M.; Schmidt-Lainé, Cl., Mathematical Modeling in Combustion and Related Topics - Proc. NATO Advanced Research Workshop. Mathematical Modeling in Combustion and Related Topics - Proc. NATO Advanced Research Workshop, 27-30 April 1987, Lyon, France (1988), Martinus Nijhoff: Martinus Nijhoff Dordrecht), 491
[15] Glowinski, R.; Golub, G. H.; Meurant, G. A.; Periaux, J., (First Intern. Symp. on Domain Decomposition Methods for Partial Differential Equations (1988), SIAM: SIAM Philadelphia)
[16] Gosman, A. D.; Pun, W. M.; Runchal, A. K.; Spalding, D. B.; Wolfshtein, M., Heat and Mass Transfer in Recirculating Flows (1969), Academic Press: Academic Press New York · Zbl 0239.76001
[17] Hageman, L. A.; Young, D. M., Applied Iterative Methods (1981), Academic Press: Academic Press New York · Zbl 0459.65014
[18] Keyes, D. E.; Gropp, W. D., SIAM J. Sci. Stat. Comput., 8, s166 (1987) · Zbl 0619.65088
[19] Keyes, D. E.; Smooke, M. D., J. Comput. Phys., 73, 267 (1987) · Zbl 0656.65111
[20] Keyes, D. E.; Smooke, M. D., (Noor, A. K., Parallel Computations and Their Impact on Mechanics (1987), Am. Soc. of Mechanical Engineers: Am. Soc. of Mechanical Engineers New York), 375
[21] Keyes, D. E.; Gropp, W. D., (Chan, T. F.; Glowinski, R.; Periaux, J.; Widlund, O., Second Intern. Symp. on Domain Decomposition Methods (1989), SIAM: SIAM Philadelphia), to appear
[22] Manteuffel, T. A., Num. Math., 28, 307 (1977) · Zbl 0361.65024
[23] Manteuffel, T. A., Num. Math., 31, 183 (1978) · Zbl 0413.65032
[24] Meierink, J. A.; van der Vorst, H. A., J. Comput. Phys., 44, 134 (1981) · Zbl 0472.65028
[25] Miller, J. A.; Kee, R. J.; Smooke, M. D.; Grcar, J. F., (Technical Report WSS/CI 84-20 (1984), The Combustion Institute), (presented at the 1984 Spring Meeting of the Western States Section of the Combustion Institute, University of Colorado, Boulder)
[26] (Noor, A. K., Parallel Computations and Their Impact on Mechanics (1987), Am. Soc. of Mechanical Engineers: Am. Soc. of Mechanical Engineers New York)
[27] (Proskurowski, W., Applied Numerical Mathematics (1989)), (special issue on domain decomposition)
[28] Saad, Y.; Schultz, M., SIAM J. Sci. Stat. Comput., 7, 856 (1986) · Zbl 0599.65018
[29] Saad, Y.; Schultz, M., (Technical Report YALEU/DCS/RR-425 (October 1985), Computer Science Dept., Yale University)
[30] Scientific Computing Associates. Scientific Computing Associates, PCGPAK User’s Guide (1984)
[31] Shakib, F.; Hughes, T. J.R.; Johan, Z., (Kane, J. H., Proc. Symp. on the Solution of Super Large Problems in Computational Mechanics (1988), Plenum: Plenum New York)
[32] Smooke, M. D., J. Comput. Phys., 48, 72 (1982) · Zbl 0492.65065
[33] Smooke, M. D.; Mitchell, R. E.; Grcar, J. F., (Birkhoff, G.; Schoenstadt, A., Elliptic Problem Solvers II (1984), Academic Press: Academic Press New York), 557
[34] Smooke, M. D.; Turnbull, A. A.; Mitchell, R. E.; Keyes, D. E., (Brauner, C. M.; Schmidt-Lainé, Cl., Mathematical Modeling in Combustion and Related Topics — Proc. NATO Advanced Research Workshop. Mathematical Modeling in Combustion and Related Topics — Proc. NATO Advanced Research Workshop, 27-30 April 1987, Lyon, France (1987), Martinus Nijhoff: Martinus Nijhoff Dordrecht), 261
[35] Walker, H. F., SIAM J. Sci. Stat. Comp., 9, 152 (1988) · Zbl 0698.65021
[36] Watts, J. W., Soc. Petrol. Engin. J., 21, 345 (1981)
[37] Widlund, O. B., (Technical Report 386 (June 1988), Courant Institute of Mathematical Sciences, NYU)
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