On Preconditioned Uzawa-type Iterations for a Saddle Point Problem with Inequality Constraints
We consider preconditioned Uzawa iterations for a saddle point problem with inequality constraints as arising from an implicit time discretization of the Cahn-Hilliard equation with an obstacle potential. We present a new class of preconditioners based on linear Schur complements associated with successive approximations of the coincidence set. In numerical experiments, we found superlinear convergence and finite termination.
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- 11.C. M. Elliott, The Cahn-Hilliard model for the kinetics of phase separation, in Mathematical models for phase change problems, J. F. Rodrigues, ed., Basel, 1989, Birkhäuser, pp. 35–73.Google Scholar
- 12.H. C. Elman and G. H. Golub, Inexact and preconditioned Uzawa algorithms for saddle point problems, SIAM J. Numer. Anal., (1994), pp. 1645–1661.Google Scholar
- 13.D. J. Eyre, An unconditionally stable one-step scheme for gradient systems, tech. rep., University of Utah, Salt Lake City, UT, 1998.Google Scholar
- 14.R. Glowinski, J. L. Lions, and R. Trémolières, Numerical Analysis of Variational Inequalities, no. 8 in Studies in Mathematics and its Applications, North-Holland Publishing Company, Amsterdam, 1981.Google Scholar
- 15.C. Gräser and R. Kornhuber, Preconditioned Uzawa iterations for the Cahn-Hilliard equation with obstacle potential. To appear.Google Scholar