A shape and topology optimization technique for solving a class of linear complementarity problems in function space

Authors:
M. Hintermüller;A. Laurain
Affiliations:
University of Sussex, Brighton, UK BN1 9RF and Department of Mathematics, and Scientific Computing, Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria 8010;Institute of Mathematics and Scientific Computing, University of Graz, Graz, Austria 8010
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

A shape and topology optimization driven solution technique for a class of linear complementarity problems (LCPs) in function space is considered. The main motivating application is given by obstacle problems. Based on the LCP together with its corresponding interface conditions on the boundary between the coincidence or active set and the inactive set, the original problem is reformulated as a shape optimization problem. The topological sensitivity of the new objective functional is used to estimate the "topology" of the active set. Then, for local correction purposes near the interface, a level set based shape sensitivity technique is employed. A numerical algorithm is devised, and a report on numerical test runs ends the paper.