A consistent frame for sensitivity filtering and the vertex assigned morphing of optimal shape

The paper discusses the filtering of shape sensitivities as a mesh independent regularization method for very large problems of shape optimal design. The vertices of the simulation discretization grids are directly used as design morphing handles allowing for the largest possible design space. Still, however, there has been a lack of theory to consistently merging the sensitivity filtering into the standard optimization technology which is an ongoing topic of discussion in the community. The actual paper tries to overcome this burden. As a result it will be shown that there is a perfect transition between the sensitivity filtering and all the other shape parameterization techniques used for the shape optimization, as there are CAD-based techniques, subdivision surfaces or morphing box technologies. It appears that sensitivity filtering belongs to the most general and powerful control technologies available for shape optimal design. The success will be demonstrated by various illustrative examples which span from basic aspects to sophisticated applications in structural and fluid mechanics.