Parallelism in ILU-preconditioned GMRES

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.