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Abstract
Chin, P. and P.A. Forsyth, A comparison of GMRES and CGSTAB accelerations for incompressible Navier-Stokes problems, Journal of Computational and Applied Mathematics 46 (1993) 415–426. Recently, incomplete LU preconditioned conjugate-gradient-type matrix solvers have been used in conjunction with Newton or Newton-like methods to solve the fully-coupled incompressible Navier-Stokes equations. A number of acceleration methods can be used for the large sparse nonsymmetric linear systems that arise from such situations. In this work, we compare GMRES and CGSTAB, a “stabilized” variant of CGS. By observing the effect of various factors (e.g., grid size, preconditioning), we attempt to determine the classes of problems to which each acceleration method is best suited. Numerical results obtained with several two-dimensional geometries are provided.
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