Extremal Rearrangement Problems Involving Poisson’s Equation with Robin Boundary Conditions
Extremal Rearrangement Problems Involving Poisson’s Equation with Robin Boundary Conditions
复制标题
DOI：
10.1007/s10915-021-01413-2
复制
发表时间：
2021-02
影响因子：
2.5
通讯作者：
C. Kao;S. Mohammadi
中科院分区：
文献类型：
--
作者：
C. Kao;S. Mohammadi
在本文中，我们研究了相应的泊松方程罗宾边界条件的最小化和最大化问题。这些重排形状优化问题出现在许多应用中，包括机械振动和流体力学的设计，探索控制总位移和动能的可能性，分别。在分析上，我们研究了一般域上极值解的性质，包括拓扑和几何。最优值的渐近行为进行了研究。虽然这类优化问题的显式解是罕见的，我们得到这样的解决方案在N-球。在数值上，我们提出了有效的算法有限元方法，重排技术和我们的分析结果的基础上，以确定在一般域上的几个迭代的极值。
In this paper, we study both minimization and maximization problems corresponding to a Poisson’s equation with Robin boundary conditions. These rearrangement shape optimization problems arise in many applications including the design of mechanical vibration and fluid mechanics that explore the possibility to control the total displacement and the kinetic energy, respectively. Analytically, we study the properties of the extremizers on general domains including topology and geometry of the optimizers. Asymptotic behaviors of the optimal values are investigated as well. Although the explicit solutions are rare for this kind of optimization problems, we obtain such solutions onN-balls. Numerically, we propose efficient algorithms based on finite element methods, rearrangement techniques and our analytical results to determine the extremizers in just a few iterations on general domains.