2021/09/04 by Antunes, Pedro R. S.
#FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2109.01884
We develop a numerical method for solving shape optimization of functionals involving Steklov eigenvalues and apply it to the problem of maximization of the k-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.