Abstract
Approximate factorisations such as the incomplete LP −1 U factorisation are notoriously sequential. We present the results of some experiments with a block-version of the ILP −1 U(0) factorisation preconditioning technique. Parallelisation of this Block ILP −1 U(0) factorisation preconditioner is straightforward: all blocks can be handled in parallel. Within the framework of an Euler/Navier-Stokes solver, we have studied the effect of introducing more blocks on the initial and the asymptotic convergence rate of a GMRES solver. The main result is that the introduction of more blocks does not lead to severe convergence degradation. Thus a high parallel efficiency can be achieved.
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References
T. J. Barth. Parallel CFD algorithms on unstructured meshes. In Special Course on Parallel Computing in CFD, pages 7.1–7.41. AGARD R-807, NATO, Neuilly-sur-Seine, France, 1995.
E. de Sturler. Incomplete block LU preconditioners on slightly overlapping sub-domains for a massively parallel computer. Technical Report CSCS-TR-94-03, Swiss Scientific Computer Center, CH-6928 Manno, Switzerland, 1994.
B. Hendrickson and R. Leland. The Chaco User's Guide, version 2.0. Sandia National Laboratories, Albuquerque, NM 87185, 1994. SAND94-2692.
E. Issman and G. Degrez. A parallel implicit compressible multidimensional upwind Euler/Navier-Stokes solver on unstructured meshes. These proceedings, 1996.
E. Issman, G. Degrez, and H. Deconinck. Implicit iterative methods for a multidimensional upwind Euler/Navier-Stokes solver on unstructured meshes, 1995. AIAA Paper 95-163, AIAA 12th CFD Conference, San Diego, CA.
H. Paillère, H. Deconinck, and P.L. Roe. Conservative upwind residual-distribution schemes based on the steady characteristic of the Euler equations, 1995. AIAA Paper 95-1700, AIAA 12th CFD Conference, San Diego, CA.
F. Stella, M. Marrone, and E. Bucchignani. A parallel preconditioned CG type method for incompressible Navier-Stokes equations. In A. Ecer, J. Hauser, P. Leca, and J. Periaux, editors, Parallel Computational Fluid Dynamics. Elsevier, Amsterdam, 1993.
Y. Saad and M. H. Schultz. GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput., 7(3):856–869, 1986.
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© 1996 Springer-Verlag Berlin Heidelberg
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Goossens, S., Issman, E., Degrez, G., Roose, D. (1996). Block ILP −1 U/(O) preconditioning for a GMRES based Euler/Navier-Stokes solver. In: Liddell, H., Colbrook, A., Hertzberger, B., Sloot, P. (eds) High-Performance Computing and Networking. HPCN-Europe 1996. Lecture Notes in Computer Science, vol 1067. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61142-8_605
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DOI: https://doi.org/10.1007/3-540-61142-8_605
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