论文标题
对形状最佳设计问题建模的连续观点
A continuous perspective on modeling of shape optimal design problems
论文作者
论文摘要
在本文中，我们将形态优化问题视为通过映射方法作为最佳控制问题。引入了参考域，而不是在一组可允许的形状上进行优化，并在一组可接受的转换上进行了优化。重点是选择集合集的选择，我们从功能空间的角度来激励。为了保证可允许转换的局部注入性，我们通过非线性约束来丰富优化问题。该方法不需要对扩展方程式进行参数调整，并且可以自然地与体积的几何约束和形状的Barycenter结合在一起。提出了阻力最小化stokes流量的数值结果。
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of admissible transformations. The focus is on the choice of the set of transformations, which we motivate from a function space perspective. In order to guarantee local injectivity of the admissible transformations we enrich the optimization problem by a nonlinear constraint. The approach requires no parameter tuning for the extension equation and can naturally be combined with geometric constraints on volume and barycenter of the shape. Numerical results for drag minimization of Stokes flow are presented.
