6 citations · 9 across the 9 of their papers we have counts for
9 papers
Quasi-Monte Carlo time-splitting methods for the Schrödinger equation with Gaussian random potential
Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao
In this paper, we study the Schrödinger equation with a Gaussian random potential (SE-GP) and develop an efficient numerical method to approximate the expectation of physical obser…
Direct Algorithms for Reconstructing Small Conductivity Inclusions in Subdiffusion
Jiho Hong, Bangti Jin, Zhizhang Wu
The subdiffusion model that involves a Caputo fractional derivative in time is widely used to describe anomalously slow diffusion processes. In this work we aim at recovering the l…
Computing large deviation rate functions of entropy production for diffusion processes by an interacting particle method
Zhizhang Wu, Renaud Raquépas, Jack Xin +1
We develop an interacting particle method (IPM) for computing the large deviation rate function of entropy production for diffusion processes, with emphasis on the vanishing-noise…
Error estimate of a quasi-Monte Carlo time-splitting pseudospectral method for nonlinear Schrodinger equation with random potentials
Zhizhang Wu, Zhiwen Zhang, Xiaofei Zhao
In this paper, we consider the numerical solution of a nonlinear Schrodinger equation with spatial random potential. The randomly shifted quasi-Monte Carlo (QMC) lattice rule combi…
Deterministic-Statistical Approach for an Inverse Acoustic Source Problem using Multiple Frequency Limited Aperture Data
Yanfang Liu, Zhizhang Wu, Jiguang Sun +1
We propose a deterministic-statistical method for an inverse source problem using multiple frequency limited aperture far field data. The direct sampling method is used to obtain a…
A Filon-Clenshaw-Curtis-Smolyak rule for multi-dimensional oscillatory integrals with application to a UQ problem for the Helmholtz equation
Zhizhang Wu, Ivan G. Graham, Dingjiong Ma +1
In this paper, we combine the Smolyak technique for multi-dimensional interpolation with the Filon-Clenshaw-Curtis (FCC) rule for one-dimensional oscillatory integration, to obtain…
A Deep Learning Approach to Nonconvex Energy Minimization for Martensitic Phase Transitions
Xiaoli Chen, Phoebus Rosakis, Zhizhang Wu +1
We propose a mesh-free method to solve nonconvex energy minimization problems for martensitic phase transitions and twinning in crystals, using the deep learning approach. These pr…
Convergence analysis of an operator-compressed multiscale finite element method for Schrödinger equations with multiscale potentials
Zhizhang Wu, Zhiwen Zhang
In this paper, we analyze the convergence of the operator-compressed multiscale finite element method (OC MsFEM) for Schrödinger equations with general multiscale potentials in the…
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…