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

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 4; pp. 5049 - 5071
Main Authors Guo, Shuangbing, Lu, Xiliang, Zhang, Zhiyue
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
eigenvalue optimization
error estimate
finite element method
schrödinger operator
shape optimization
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022281