The Mathematical Institute, University of Oxford, Eprints Archive

Fast Solvers for Cahn-Hilliard Inpainting

Bosch, Jessica and Kay, David and Stoll, Martin and Wathen, A. J. (2013) Fast Solvers for Cahn-Hilliard Inpainting. Technical Report. SIAM. (Submitted)

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Abstract

We consider the efficient solution of the modified Cahn-Hilliard equation for binary image inpainting using convexity splitting, which allows an unconditionally gradient stable time-discretization scheme. We look at a double-well as well as a double obstacle potential. For the latter we get a nonlinear system for which we apply a semi-smooth Newton method combined with a Moreau-Yosida regularization technique. At the heart of both methods lies the solution of large and sparse linear systems. We introduce and study block-triangular preconditioners using an efficient and easy to apply Schur complement approximation. Numerical results indicate that our preconditioners work very well for both problems and show that qualitatively better results can be obtained using the double obstacle potential.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Information and communication, circuits
H - N > Mechanics of deformable solids
O - Z > Partial differential equations
A - C > Computer science
A - C > Classical thermodynamics, heat transfer
O - Z > Systems theory
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1705
Deposited By: Lotti Ekert
Deposited On:26 Jun 2013 08:13
Last Modified:29 May 2015 19:24

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