115 citations · 208 across the 17 of their papers we have counts for
9 papers · 1 filter
Approximation and Generalization of DeepONets for Learning Operators Arising from a Class of Singularly Perturbed Problems
Ting Du, Zhongyi Huang, Ye Li
Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator…
A Uniform Convergent Petrov-Galerkin method for a Class of Turning Point Problems
Li Feng, Zhongyi Huang
In this paper, we propose a numerical method for turning point problems in one dimension based on Petrov-Galerkin finite element method (PGFEM). We first give a priori estimate for…
Seismic Tomography with Random Batch Gradient Reconstruction
Yixiao Hu, Lihui Chai, Zhongyi Huang +1
Seismic tomography solves high-dimensional optimization problems to image subsurface structures of Earth. In this paper, we propose to use random batch methods to construct the gra…
Artificial boundary method for the solution of pricing European options under the Heston model
Hongshan Li, Zhongyi Huang
This paper considers the valuation of a European call option under the Heston stochastic volatility model. We present the asymptotic solution to the option pricing problem in power…
A Bloch decomposition-based stochastic Galerkin method for quantum dynamics with a random external potential
Zhizhang Wu, Zhongyi Huang
In this paper, we consider the numerical solution of the one-dimensional Schrödinger equation with a periodic lattice potential and a random external potential. This is an importan…
Numerical simulations of X-rays Free Electron Lasers (XFEL)
Paolo Antonelli, Agissilaos Athanassoulis, Zhongyi Huang +1
We study a nonlinear Schrödinger equation which arises as an effective single particle model in X-ray Free Electron Lasers (XFEL). This equation appears as a first-principles model…
Gaussian Beam Methods for the Dirac Equation in the Semi-classical Regime
Hao Wu, Zhongyi Huang, Shi Jin +1
The Dirac equation is an important model in relativistic quantum mechanics. In the semi-classical regime , even a spatially spectrally accurate time splitting method \cite{H…
A Bloch decomposition based split-step pseudo spectral method for quantum dynamics with periodic potentials
Zhongyi Huang, Shi Jin, Peter Markowich +1
We present a new numerical method for accurate computations of solutions to (linear) one dimensional Schrödinger equations with periodic potentials. This is a prominent model in so…
A time-splitting spectral scheme for the Maxwell-Dirac system
Zhongyi Huang, Shi Jin, Peter Markowich +2
We present a time-splitting spectral scheme for the Maxwell-Dirac system and similar time-splitting methods for the corresponding asymptotic problems in the semi-classical and the…