论文标题
pdes表面上的拓扑导数
Topological derivative for PDEs on surfaces
论文作者
论文摘要
在本文中，我们研究了在$ \ Mathbf r^d $中，在$ \ mathbf r^d $中，通过拓扑衍生衍生剂的方式，在光滑的子手机上$ m $ d-1 $的最佳分布的问题。我们考虑一类形状优化问题，这些问题受到表面上线性偏微分方程的约束。我们检查了差分操作员和材料系数的奇异扰动，并得出拓扑衍生物。最后，我们展示了如何将表面上的拓扑导数与表面上的水平集方法结合起来来数值来解决拓扑优化问题。
In this paper we study the problem of the optimal distribution of two materials on smooth submanifolds $M$ of dimension $d-1$ in $\mathbf R^d$ without boundary by means of the topological derivative. We consider a class of shape optimisation problems which are constrained by a linear partial differential equation on the surface. We examine the singular perturbation of the differential operator and material coefficients and derive the topological derivative. Finally, we show how the topological derivative in conjunction with a level set method on the surface can be used to solve the topology optimisation problem numerically.
