Memorandum 1786

A class of nonsymmetric preconditioners for saddle point problems

M.A. Botchev & G.H. Golub

For the iterative solution of saddle point problems, a nonsymmetric preconditioner is studied which, with respect to the upper-left block of the system matrix, can be seen as a variant of SSOR. An idealized situation where SSOR is taken with respect to the skew-symmetric part plus the diagonal part of the upper-left block is analyzed in detail. Since action of the preconditioner involves solution of a Schur complement system, an inexact form of the preconditioner can be of interest. This results in an inner-outer iterative process. Numerical experiments with solution of linearized Navier-Stokes equations demonstrate the efficiency of the new preconditioner, especially when the left-upper block is far from symmetric.

Keywords:   Saddle point problem, iterative method, preconditioning method, nonsymmetric indefinite linear systems, SSOR, constraint preconditioner, skew-symmetric preconditioner, inner-outer iterations, Navier-Stokes equations

Mathematics Subject Classification:   65F10, 65F22, 65F35, 65N22, 65K10

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