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曹锡华数学论坛 - 计算数学分论坛
From shape optimization to preshape calculus
Volker Schulz 教授(德国特里尔大学)
2021年5月19日16:00-17:00  Zoom

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Shape optimization is a very active field of research. This talk discusses, on the one hand, fast methods for the solution of PDE constrained shape optimization problems in certain fields of application, based on the shape calculus. On the other hand, algorithmic shape optimization is usually geared to the generation of successive normal deformations of shapes towards optimality criteria. Often, this stretches surfaces in tangential direction leading to misbalanced surface meshes. Indeed, the shape derivative does not give any information in tangential direction at all, which means that tangential deformations can be used for other practical purposes without compromising optimality. A broader perspective thus leads to a natural generalization of the classical shape calculus to pre-shape calculus, as we would like to call it. Motivation of this concept together with first theoretical and numerical results are presented.

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