论文标题
形状优化中的隐式参数化：边界观察
Implicit parametrizations in shape optimization: boundary observation
论文作者
论文摘要
我们首先对现有文献进行了有关形状优化的简要回顾，这强调了最近在拓扑优化中使用哈密顿系统。在第二部分中，我们收集了有关隐式参数定理的一些初步，尤其是在第二个维度中，这是一种对形状优化感兴趣的情况。还讨论了该问题的表述。第3节中分析了通过惩罚及其可不同性能的近似值。接下来，我们研究了第4节中的离散过程。最后一节致力于数值实验。
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.
