Semismooth Newton Methods: Theory, Numerics, and Applications

ao. Univ.-Prof. Dipl.-Ing. Dr. Michael Hinterm├╝ller

Aug. 1, 2005, noon HF 9904

Recently it was found that semismooth Newton methods are highly efficient numerical solution techniques for certain classes of complementarity and variational inequality problems in function space. Particular realizations can be easily implemented as primal-dual active set strategies, and they are widley applicable in practice.

The aim of this talk is to discuss the state-of-the-art in semismooth Newton methods for function space problems. Among others, the main topics that will be addressed are finite vs. infinite dimensional methods and a suitable generalized differential, convergence theory - fast local convergence and rate of convergence, mesh independence, special problem classes yielding global convergence, path-following semismooth Newton concepts in case of low regularity, full multigrid acceleration, and applications ranging from optimal control of partial differential equations, obstacle problems, over contact and crack problems to problems in image restoration.