Parameter-Free Shape Optimization: Various Shape Updates for Engineering Applications

In the last decade, parameter-free approaches to shape optimization problems have matured a state where they provide versatile tool for complex engineering applications. However, sensitivity distributions obtained from derivatives in this context cannot be directly used as update gradient-based strategies. Instead, an auxiliary problem has solved obtain gradient sensitivity. While several choices these were investigated mathematically, complexity of concepts behind their derivation often prevented application engineering. This work aims explain compute updates perspective. We introduce corresponding formal way and compare by means numerical examples. To end, test case exemplary applications computational fluid dynamics are considered.