Project C4 (finished)

Project C4 - Shape optimization with the embedded domain technique

Principal Investigator: Michael Hinze

Scientific Background and Motivation

Shape optimization plays an important role in many fluid mechanic applications and certainly  may be considered as one of the most important drivers for the use of simulation approaches in fluids-engineering industry. When many design parameters are involved, the computational effort for the optimization of an existing shape with  with brut-force methods quickly becomes prohibitive. Here, adjoint methods offer an elegant alternative. These methods allow to express the derivatives of cost functionals with the help of adjoint variables. In many approaches, the shape only enters implicitly into the design process through parametrizations of the domain by grids. Here, we consider shapes which are parametrized by curves, whose parametrizations are considered as optimization variables in the optimization process. This allows a direct access to the design variables during the optimization procedure.

Aims and Objectives

To tackle real world shape optimizaiton applications fast solution methods are needed which are able to treat problems with arbitrarily many design variables. This is the focal point of the project, which we approach through the development of an adjoint shape-optimisation technique which allows a direct access to the design in the optimization process. We consider shapes parametrized by injective curves and exclude topology changes in this way. The flow problem is treated with the embedding domain technique, where the domain together with the shape is embedded into a larger, simpler reference domain, on which then the analysis and the computations are performed.

Phd student: Thorben Vehling

Thorben Vehling successfully defended his PhD on 13 April 2016.

More details can be found here.