Progress Report for the period 2003 - 2007

	Thickness optimization of a frame.
	Shape optimization of an electromagnet.
	3D topology optimization of a cantilever beam.
	2D topology optimization of a beam with local stress constraints.

The subject of this project is the development, analysis and implementation of numerically efficient algorithms for solving optimal design problems. Our approach aims at a uniform algorithm involving both, direct simulation and optimization. The application of hierarchical methods seems to be the right approach if optimal algorithms are sought. Nested algorithms similar to nested Newton iterations in the nonlinear case allow only a few iterations on finer grids wheras most of the iterations are realized on coarser grids where the solution of the direct problem is cheap. Additionally, optimal design problems cause the need for handling parameter-dependent geometries. Furthermore, adaptive strategies based on error estimated should be applied in order to reduce the total complexity of the discrete problems.

• Preprocessing: Definition of characteristic quantities, design parameters and constraints.
• Handling of parameter-dependent geometries and developing stable and efficient mesh moving strategies.
• Hierarchical optimization similar to nested Newton iterations in the nonlinear case.
• All-at-once strategies for optimal design problems with large design spaces, e.g. topology optimization.
• Coupling of shape and topology optimization.

List of Publications.