Optimizing Variational Inequalities on Shape Manifolds
Shape optimization is of importance in many fields of applications similarly to
variational inequalities. However, shape optimization problems with
constraints consisting of variational inequalities have not yet been
considered much in the existing literature. This proposal aims at a novel
approach to shape optimization problems in terms of shape manifolds and
the resulting framework from infinite dimensional Riemannian geometry,
which has been developed recently by the applicant. This approach enables
a theoretical connection of shape optimization with optimal control problems
in vector bundles, which will be the guiding principle for the analytical and
numerical investigations within this project. Thus, the goals of this project are
investigations in the area of shape optimization for variational inequalities
regarding appropriate Riemannian shape manifold formulations, existence
and well-posedness of solutions, semi-smoth Newton methods on shape
vector bundles, mesh independent algorithmic approaches, robust treatment
of uncertainties and solution approaches to application problems from the
field of (thermo-)mechanics. Besides that, the shape manifold approach
together with its novel shape metrics enhancing discretization and
algorithmic robustness provides a basis for cooperation with other projects
addressing shape based problem formulations.
No publications from this project yet.
No preprints from this project yet.