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An algebraic multilevel parallelizable preconditioner for large-scale CFD problems. (English) Zbl 0923.76247

Summary: An efficient parallelizable preconditioner for solving large-scale CFD problems is presented. It is adapted to coarse-grain parallelism and can be used for both shared and distributed-memory parallel computers. The proposed preconditioner consists of two independent approximations of the system matrix. The first one is a block-diagonal, fully parallelizable approximation of the given system. The second matrix is coarser than the original one and is built using algebraic multi-grid methods. The preconditioner is used to compute the steady solution of the compressible Navier-Stokes equations for subsonic laminar flows, on shared-memory computers, for a moderate number of processors. The coupled two-level preconditioner is robust and has a large potential for parallelism. Interesting savings in computational time for parallel computations are obtained when comparing the two-level preconditioner with the well-known incomplete Gaussian factorization.

MSC:

76M99 Basic methods in fluid mechanics
76M10 Finite element methods applied to problems in fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65Y05 Parallel numerical computation

Software:

Chaco
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References:

[1] Cuthill, E.H.; McKee, J.M., Reducing the bandwith of sparse symmetric matrices, (), 157-172
[2] Dutto, L.C., The effect of ordering on preconditioned GMRES algorithm, for solving the compressible Navier-Stokes equations, Int. J. numer. methods engrg., 36, 3, 457-497, (1993) · Zbl 0767.76026
[3] Dutto, L.C.; Habashi, W.G.; Fortin, M., Parallelizable block diagonal preconditioners for the compressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 117, 15-47, (1994) · Zbl 0847.76032
[4] Dutto, L.C.; Habashi, W.G.; Robichaud, M.P.; Fortin, M., A method for finite element parallel viscous compressible flow calculations, Int. J. numer. methods in fluids, 19, 275-294, (1994) · Zbl 0815.76042
[5] Freund, R.W., A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. sci. comput., 14, 2, 470-482, (1993) · Zbl 0781.65022
[6] Also as Research Report STAN CS-71-208, Stanford University, Stanford, USA.
[7] George, A.; Liu, J.W.H., The evolution of the minimum degree ordering algorithm, SIAM rev., 31, 1-19, (1989) · Zbl 0671.65024
[8] Hendrickson, B.; Leland, R., The chaco User’s guide, version 1.0, (), NM 87185-1110
[9] Hendrickson, B.; Leland, R., A multilevel algorithm for partitioning graphs, ()
[10] Lepage, C., A guide to FENSAP, version 3.6, ()
[11] Liu, W.-H.; Sherman, A.H., Comparative analysis of the cuthill-mckee and the reverse cuthill-mckee ordering algorithms for sparse matrices, SIAM J. numer. anal., 13, 2, 198-213, (1976) · Zbl 0331.65022
[12] Martin, G., Méthodes de préconditionnement par factorisation incomplète, ()
[13] O’Neil, J.; Szyld, D.B., A block ordering method for sparse matrices, SIAM J. sci. stat. comput., 11, 5, 811-823, (1990) · Zbl 0706.65021
[14] Robichaud, M.P.; Habashi, W.G.; Peeters, M.F.; Dutto, L.C.; Fortin, M., Parallel finite element computation of 3D compressible turbomachinery flows on workstation clusters, (), 41-56
[15] Robitaille, C., Une expérience de parallélisation d’un code d’eléments finis, ()
[16] Saad, Y.; Schultz, M., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. sci. stat. comput., 7, 3, 856-869, (1986) · Zbl 0599.65018
[17] Sonneveld, P., CGS, a fast Lanczos type solver for nonsymmetric linear systems, SIAM J. sci. stat. comput., 10, 36-52, (1989) · Zbl 0666.65029
[18] van der Vorst, H.A., Bi-CGSTAB: A fast and smoothly converging variant of bi-CG for the solution of nonsymmetric linear systems, SIAM J. sci. stat. comput., 13, 631-644, (1992) · Zbl 0761.65023
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