14 citations · 37 across the 8 of their papers we have counts for
11 papers · 1 filter
A potential projection method for the nonlinear Schrödinger equation with low regularity potential
Weizhu Bao, Qingyuan Sun, Chushan Wang
We propose a potential projection (PP) method for the nonlinear Schrödinger equation (NLSE) with low-regularity and singular potentials by replacing the potential with its Fourier…
A spectral-element method for computing many eigenvalues and their asymptotics of the Schrödinger operator with Robin boundary condition
Weizhu Bao, Fukeng Huang
We propose spectral and spectral-element methods for accurately computing many eigenvalues of the Schrödinger operator with Robin boundary condition on simple and complex geometrie…
Optimal error bounds on the exponential wave integrator for nonlinear Schrödinger equations with highly singular potential
Weizhu Bao, Chushan Wang, Yifei Wu
We establish error estimates of the first-order exponential wave integrator (EWI) for the nonlinear Schrödinger equation (NLSE) with a highly singular potential in w…
Error estimates of an exponential wave integrator for the nonlinear Schrödinger equation with singular potential
Weizhu Bao, Chushan Wang
We analyze a first-order exponential wave integrator (EWI) for the nonlinear Schrödinger equation (NLSE) with a singular potential that is locally in , which might be locally…
Optimal error bounds on an exponential wave integrator Fourier spectral method for the logarithmic Schrödinger equation
Weizhu Bao, Ying Ma, Chushan Wang
We prove a nearly optimal error bound on the exponential wave integrator Fourier spectral (EWI-FS) method for the logarithmic Schrödinger equation (LogSE) under the assumption of $…
A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices
Qingyuan Shi, Yongyong Cai, Chijie Zhuang +4
Solving real-world nonlinear semiconductor device problems modeled by the drift-diffusion equations coupled with the Poisson equation (also known as the Poisson-Nernst-Planck equat…
An extended Fourier pseudospectral method for the Gross-Pitaevskii equation with low regularity potential
Weizhu Bao, Bo Lin, Ying Ma +1
We propose and analyze an extended Fourier pseudospectral (eFP) method for the spatial discretization of the Gross-Pitaevskii equation (GPE) with low regularity potential by treati…
An explicit and symmetric exponential wave integrator for the nonlinear Schrödinger equation with low regularity potential and nonlinearity
Weizhu Bao, Chushan Wang
We propose and analyze a novel symmetric Gautschi-type exponential wave integrator (sEWI) for the nonlinear Schrödinger equation (NLSE) with low regularity potential and typical po…
Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential
Weizhu Bao, Yongyong Cai, Jia Yin
Super-resolution of the Lie-Trotter splitting () and Strang splitting () is rigorously analyzed for the nonlinear Dirac equation without external magnetic potentials in t…
A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime
Weizhu Bao, Yongyong Cai, Xiaofei Zhao
We propose and analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for solving the Klein-Gordon (KG) equation with a dimensionless parameter $0<\varepsilon\…
Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrodinger equation with wave operator
Weizhu Bao, Yongyong Cai
We propose an exponential wave integrator sine pseudospectral (EWI-SP) method for the nonlinear Schrödinger equation (NLS) with wave operator (NLSW), and carry out rigorous error a…