A Numerical Study of Steklov Eigenvalue Problem via Conformal Mapping
Numerical Analysis
2018-05-08 v1
Abstract
In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov eigenvalue problem in the complex domain via conformal mappings. The eigenfunctions are expanded in Fourier series so the discretization leads to an eigenvalue problem for coefficients of Fourier series. For shape optimization problem, we use the gradient ascent approach to find the optimal domain which maximizes th Steklov eigenvalue with a fixed area for a given . The coefficients of Fourier series of mapping functions from a unit circle to optimal domains are obtained for several different
Cite
@article{arxiv.1805.01959,
title = {A Numerical Study of Steklov Eigenvalue Problem via Conformal Mapping},
author = {Weaam Alhejaili and Chiu-Yen Kao},
journal= {arXiv preprint arXiv:1805.01959},
year = {2018}
}