Morfologibaserad rigorös geometrihantering för randeffektsdominerade konstruktionsoptimeringsproblem

This project primarily investigates questions regarding geometric properties, in particular, boundary identification and treatment in the context of computational design optimization.

The primary objectives are to:* Extend the theory for morphological operators and develop approximate morphological operators.* Develop and analyze methods that allow for rigorous geometry handling and use these to solve boundary-effect dominated problems.* Establish new ways to deal with and solve various applied problems, such as cases with manufacturing uncertainty.To achieve the above objectives, this project will expand the theory concerning morphological operators and adapt it to a measure-theoretic/functional-analytic framework.

Here we will, in addition, develop approximate morphological operators and use them as a fundamental component in new design optimization methods---for example, to create boundary indicator functions and use them to solve boundary-effect dominated problems.Altogether, this project will expand the theoretical foundation and the applicability area of numerical design optimization methods.

Preliminary results demonstrate that it is possible to create novel numerical design optimization methods—based on ideas and theory that will be further explored and expanded in this project—that outperform contemporary state-of-the-art.