33 citations · 80 across the 13 of their papers we have counts for
13 papers
A Semi-definite Optimization Method for Maximizing the Shared Band Gap of Topological Photonic Crystals
Chiu-Yen Kao, Junshan Lin, Braxton Osting
Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator…
Steklov Eigenvalue Problems on Nearly Spherical and Nearly Annular Domains
Nathan Schroeder, Weaam Alhejaili, Chiu-Yen Kao
We consider Steklov eigenvalues on nearly spherical and nearly annular domains in dimensions. By using the Green-Beltrami identity for spherical harmonic functions, the derivat…
Harmonic functions on finitely-connected tori
Chiu-Yen Kao, Braxton Osting, Édouard Oudet
In this paper, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whos…
Flat tori with large Laplacian eigenvalues in dimensions up to eight
Chiu-Yen Kao, Braxton Osting, Jackson C. Turner
We consider the optimization problem of maximizing the -th Laplacian eigenvalue, , over flat -dimensional tori of fixed volume. For , this problem is equivalent t…
Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems
Chiu-Yen Kao, Braxton Osting, Èdouard Oudet
Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary mini…
Extremal Spectral Gaps for Periodic Schrödinger Operators
Chiu-Yen Kao, Braxton Osting
The spectrum of a Schrödinger operator with periodic potential generally consists of bands and gaps. In this paper, for fixed m, we consider the problem of maximizing the gap-to-mi…
A Numerical Study of Steklov Eigenvalue Problem via Conformal Mapping
Weaam Alhejaili, Chiu-Yen Kao
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 ap…
A New Algorithm to Simulate the First Exit Times of a Vector of Brownian Motions, with an Application to Finance
Chiu-Yen Kao, Qidi Peng, Henry Schellhorn +1
We provide a new methodology to simulate the first exit times of a vector of Brownian motions from an orthant. This new approach can be used to simulate the first exit times of dim…
Computational Methods For Extremal Steklov Problems
Eldar Akhmetgaliyev, Chiu-Yen Kao, Braxton Osting
We develop a computational method for extremal Steklov eigenvalue problems and apply it to study the problem of maximizing the -th Steklov eigenvalue as a function of the domain…
Maximization of Laplace-Beltrami eigenvalues on closed Riemannian surfaces
Chiu-Yen Kao, Rongjie Lai, Braxton Osting
Let be a connected, closed, orientable Riemannian surface and denote by the -th eigenvalue of the Laplace-Beltrami operator on . In this paper, we cons…
Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations
Xiaobing Feng, Chiu-Yen Kao, Thomas Lewis
This paper develops a new framework for designing and analyzing convergent finite difference methods for approximating both classical and viscosity solutions of second order fully…
Bounded domain problem for the modified Buckley-Leverett equation
Ying Wang, Chiu-Yen Kao
The focus of the present study is the modified Buckley-Leverett (MBL) equation describing two-phase flow in porous media. The MBL equation differs from the classical Buckley-Levere…
Numerical study of the KP equation for non-periodic waves
Chiu-Yen Kao, Yuji Kodama
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact s…