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Factorization of the incompressible Stokes operator linking pressure andvelocity is revisited. The main purpose is to use the inverse of the Stokesoperator with a large time step as a preconditioner for Newton and Arnoldiiterations applied to computation of steady three-dimensional flows and tostudy of their stability. It is shown that the Stokes operator can be inversedwithin an acceptable computational effort. This inverse includes fast directinverses of several Helmholtz operators and iterative inverse of the pressurematrix. It is shown, additionally, that fast direct solvers can be attractivefor the inverse of the Helmholtz and Laplace operators on fine grids and atlarge Reynolds numbers, as well as for other problems where convergence ofiterative methods slows down. Implementation of the Stokes operator inverse totime-stepping-based formulation of the Newton and Arnoldi iterations isdiscussed.

On direct inverse of Stokes, Helmholtz and Laplacian operators in view of time-stepper-based Newton and Arnoldi solvers in incompressible CFD