论文标题
形状前微积分：基础和应用网状质量优化的应用
Pre-Shape Calculus: Foundations and Application to Mesh Quality Optimization
论文作者
论文摘要
由优化程序引起的计算网格的变形通常会导致网格质量甚至破坏网格的变形。我们提出了一个理论框架，使用预形状来概括经典形状优化和演算。我们定义了形状的衍生物，并根据结构和微积分定理得出。特别是，与仅具有正常方向的经典形状衍生物相比，切向方向以形状衍生物为特征。经典形状优化和-calculus的技术已显示为该框架。引入了针对网格质量的优化问题类别，可以通过使用前形衍生物来解决。该类允许同时优化经典形状的目标和网格质量，而不会降低经典形状优化解决方案。新技术将实施并进行数值测试，以用于2D和3D。
Deformations of the computational mesh arising from optimization routines usually lead to decrease of mesh quality or even destruction of the mesh. We propose a theoretical framework using pre-shapes to generalize classical shape optimization and calculus. We define pre-shape derivatives and derive according structure and calculus theorems. In particular, tangential directions are featured in pre-shape derivatives, in contrast to classical shape derivatives featuring only normal directions. Techniques from classical shape optimization and -calculus are shown to carry over to this framework. An optimization problem class for mesh quality is introduced, which is solvable by use of pre-shape derivatives. This class allows for simultaneous optimization of classical shape objectives and mesh quality without deteriorating the classical shape optimization solution. The new techniques are implemented and numerically tested for 2D and 3D.
