@article{Guo2022, 
author = {Shuangbing Guo and Xiliang Lu and Zhiyue Zhang},
title = {Finite element method for an eigenvalue optimization problem of the Schrödinger operator},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {4},
pages = {5049-5071},
keywords = {eigenvalue optimization, Schrödinger operator, shape optimization, finite element method, error estimate},
url = {https://www.sciopen.com/article/10.3934/math.2022281},
doi = {10.3934/math.2022281},
abstract = {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.}
}