Report for the period 2003 - 2007
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
- Preprocessing: Definition of characteristic quantities,
design parameters and constraints.
- Handling of parameter-dependent geometries and
developing stable and efficient mesh moving
- 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.
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SpezialForschungsBereich SFB F013 | Special Research
Program of the FWF - Austrian Science Fund