论文标题
形状优化的线性视图
A Linear View on Shape Optimization
论文作者
论文摘要
形状不能定义线性空间。本文探讨了变形的线性结构作为形状的表示。这将形状优化转换为最佳控制的变体。突出显示了这种观点的数值挑战，并提出了第二个形状衍生物的新型线性版本，导致形状牛顿类型的特定算法。
Shapes do not define a linear space. This paper explores the linear structure of deformations as a representation of shapes. This transforms shape optimization to a variant of optimal control. The numerical challenges of this point of view are highlighted and a novel linear version of the second shape derivative is proposed leading to particular algorithms of shape Newton type.
