Spectral properties of primal-based penalty preconditioners for saddle point problems
Journal of Computational and Applied Mathematics(2010)
Abstract
For large and sparse saddle point linear systems, this paper gives further spectral properties of the primal-based penalty preconditioners introduced in [C.R. Dohrmann, R.B. Lehoucq, A primal-based penalty preconditioner for elliptic saddle point systems, SIAM J. Numer. Anal. 44 (2006) 270–282]. The regions containing the real and non-real eigenvalues of the preconditioned matrix are obtained. The model of the Stokes problem is supplemented to illustrate the theoretical results and to test the quality of the primal-based penalty preconditioner.
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Key words
Saddle point problem,Block preconditioner,Eigenvalue,Krylov subspace method
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