论文标题
Neumann边界条件的形状优化问题的周期性哈密顿系统
Periodic Hamiltonian systems in shape optimization problems with Neumann boundary conditions
论文作者
论文摘要
使用最佳控制理论，基于Hamiltonian系统和隐式参数\ -Za \ -tion定理的方法提供了形状优化问题中的一般固定域近似方法。在以前的工作中，我们检查了Dirichlet边界条件，并进行了分布或边界观察。在这里，我们讨论了Neumann边界条件的案例，具有组合成本功能，包括分布式和边界观察。可能扩展到非线性状态系统。这项新技术允许同时进行边界和拓扑变化，我们还报告了确认理论结果的数值实验。
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have examined Dirichlet boundary conditions with distributed or boundary observation. Here, we discuss the case of Neumann boundary conditions, with a combined cost functional, including both distributed and boundary observation. Extensions to nonlinear state systems are possible. This new technique allows simultaneous boundary and topological variations and we also report numerical experiments confirming the theoretical results.
