Author:
Guo Shuangbing, ,Lu Xiliang,Zhang Zhiyue, ,
Abstract
<abstract><p>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.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference46 articles.
1. A. Henrot, Extremum problems for eigenvalues of elliptic operators, Basel: Springer, 2006.
2. G. Allaire, Shape optimization by the homogenization method, Basel: Springer, 2012.
3. C. Anedda, G. Porru, Symmetry breaking and other features for eigenvalue problems, Dynamical Systems and Differential Equations, AIMS Proceedings 2011 Proceedings of the 8th AIMS International Conference (Dresden, Germany), 2011, 61–70. https://doi.org/10.3934/proc.2011.2011.61
4. P. R. S. Antunes, S. A. Mohammadi, H. Voss, A nonlinear eigenvalue optimization problem: Optimal potential functions, Nonlinear Anal.-Real, 40 (2018), 307–327, https://doi.org/10.1016/j.nonrwa.2017.09.003
5. X. L. Bai, F. Li, Optimization of species survival for logistic models with non-local dispersal, Nonlinear Anal.-Real, 21 (2015), 53–62. https://doi.org/10.1016/j.nonrwa.2014.06.006