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An Adaptive Finite Element Moreau-Yosida-based Solver for a Non-smooth Cahn-Hilliard Problem

Tuesday, October 2, 3:30PM – 5PM
ACE 6.304

Michael Hintermueller

An adaptive finite element semi-smooth Newton solver for the Cahn-Hilliard model with double obstacle free energy is proposed. For this purpose, the governing system is discretised in time using a semi-implicit scheme, and the resulting time-discrete system is formulated as an optimal control problem with pointwise constraints on the control. For the numerical solution of the optimal control problem, we propose a function space based algorithm which combines a Moreau-Yosida regularization technique for handling the control constraints with a semi-smooth-Newton method for solving the optimality systems of the resulting sub-problems.

Further, for the discretization in space and in connection with the proposed algorithm, an adaptive finite element method is considered. The performance of the overall algorithm is illustrated by numerical experiments.

Biography Michael Hintermueller is a MATHEON Research Professor and holds a chair in Applied Mathematics at the Department of Mathematics of Humboldt-University of Berlin, Germany. From 2007-2008 he held a Chair in Applied Mathematics at the University of Sussex, UK and a visiting Associate Professorship at Rice University, in Houston, TX, in 2003-2004. Before, he was an assistant and then associate professor at the University of Graz, Austria. He is a member of the Austrian Academy of Sciences, and received the START-prize from the Austrian Ministry of Science and Education and the SIAM Best Paper Award. His main research areas are algorithms and adaptive discretization for optimization problems with partial differential equation or variational inequality constraints, shape and topology optimization, and image processing.

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