Numerical calculation of extremal Steklov eigenvalues in 3D and 4D
Optimization and Control
2021-09-07 v1
Abstract
We develop a numerical method for solving shape optimization of functionals involving Steklov eigenvalues and apply it to the problem of maximization of the -th Steklov eigenvalue, under volume constraint. A similar study in the planar case was addressed in [E. Akhmetgaliyev, C.-Y. Kao and B. Osting, SIAM J. Control Optim. 55(2), 1226-1240, (2017)] using the boundary integral equation method. Here we extend that study to the 3D and 4D cases, using the Method of Fundamental Solutions as forward solver.
Cite
@article{arxiv.2109.01884,
title = {Numerical calculation of extremal Steklov eigenvalues in 3D and 4D},
author = {Pedro R. S. Antunes},
journal= {arXiv preprint arXiv:2109.01884},
year = {2021}
}