形状optimization中的隐式参数化：边界观测
Implicit parametrizations in shape optimization: boundary observation
摘要：
我们首先简要回顾了现有的文献形状优化，强调最近使用的哈密顿系统的拓扑优化。在第二部分中，我们收集了一些关于隐式参数化定理的知识，特别是在二维中，这是形状优化中的一个有趣的例子。文中还讨论了问题的提法。在第三节中分析了通过惩罚的逼近及其可微性。接下来，我们研究第4节中的离散化过程。最后一节致力于数值实验。
英文摘要：
We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization theorem, especially in dimension two, which is a case of interest in shape optimization. The formulation of the problem is also discussed. The approximation via penalization and its differentiability properties are analyzed in Section 3. Next, we investigate the discretization process in Section 4. The last section is devoted to numerical experiments.
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