Finite element method for an eigenvalue optimization problem of the Schrödinger operator

AIMS Mathematics

Shuangbing Guo¹  Zhiyue Zhang²  Xiliang Lu³ 

[1] 1. School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang, 453003, China 2. School of Mathematical Science, Nanjing Normal University, Nanjing, 210023, China;2. School of Mathematical Science, Nanjing Normal University, Nanjing, 210023, China;3. School of Mathematics and Statistics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China;

关键词: eigenvalue optimization;    schrödinger operator;    shape optimization;    finite element method;    error estimate;   

DOI  :  10.3934/math.2022281

来源: DOAJ

【 摘 要 】

In this paper, we study the optimization algorithm to compute the smallest eigenvalue of the Schrödinger operator with volume constraint. A finite element discretization of this problem is established. We provide the error estimate for the numerical solution. The optimal solution can be approximated by a fixed point iteration scheme. Then a monotonic decreasing algorithm is presented to solve the eigenvalue optimization problem. Numerical simulations demonstrate the efficiency of the method.

【 授权许可】

Unknown