Parallelism in ILU-preconditioned GMRES |
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Authors: | C Vuik RRP van Nooyen P Wesseling |
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Affiliation: | aTechnische Wiskunde & Inform. Technische Universiteit Delft, P.O. Box 5031, 2600 GA Delft, The Netherlands;bFaculty of Civil Engineering, Delft University of Technology, P.O. Box 5048, NL 2600 GA Delft, The Netherlands |
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Abstract: | A parallel implementation of the preconditioned GMRES method is described. The method is used to solve the discretized incompressible Navier–Stokes equations. A parallel implementation of the inner product is given, which appears to be scalable on a massively parallel computer. The most difficult part to parallelize is the ILU-preconditioner. We parallelize the preconditioner using ideas proposed by Bastian and Horton (P. Bastian, G. Horton, SIAM. J. Stat. Comput. 12 (1991) 1457–1470). Contrary to some other parallel methods, the required number of iterations is independent of the number of processors used. A model is presented to predict the efficiency of the method. Experiments are done on the Cray T3D, computing the solution of a two-dimensional incompressible flow. Predictions of computing time show good correspondence with measurements. |
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Keywords: | Parallel ILU preconditioner Distributed memory computer Parallel performance model Computational fluid dynamics |
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