Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations

A new Lagrange multiplier approach for gradient flows

(2020) Qing Cheng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Energy-preserving methods for nonlinear Schrödinger equations

(2020) Christophe Besse et al.   IMA JOURNAL OF NUMERICAL ANALYSIS

Error Estimates of a Regularized Finite Difference Method for the Logarithmic Schrödinger Equation

(2019) Weizhu Bao et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable

(2019) Lianlei Lin et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions

(2019) Wenjun Cai et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein Condensates

(2019) Qingqu Zhuang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Highly Efficient and Accurate Numerical Schemes for the Epitaxial Thin Film Growth Models by Using the SAV Approach

(2018) Qing Cheng et al.   JOURNAL OF SCIENTIFIC COMPUTING

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

(2018) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Efficient spectral computation of the stationary states of rotating Bose–Einstein condensates by preconditioned nonlinear conjugate gradient methods

(2017) Xavier Antoine et al.   JOURNAL OF COMPUTATIONAL PHYSICS

High-order IMEX-spectral schemes for computing the dynamics of systems of nonlinear Schrödinger/Gross–Pitaevskii equations

(2016) Xavier Antoine et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Mean-field regime and Thomas–Fermi approximations of trapped Bose–Einstein condensates with higher-order interactions in one and two dimensions

(2016) Xinran Ruan et al.   JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS

A Fourier pseudospectral method for the “good” Boussinesq equation with second-order temporal accuracy

(2014) Kelong Cheng et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Computational methods for the dynamics of the nonlinear Schrödinger/Gross–Pitaevskii equations

(2013) Xavier Antoine et al.   COMPUTER PHYSICS COMMUNICATIONS

Robust and efficient preconditioned Krylov spectral solvers for computing the ground states of fast rotating and strongly interacting Bose–Einstein condensates

(2013) Xavier Antoine et al.   JOURNAL OF COMPUTATIONAL PHYSICS

A Simple and Efficient Numerical Method for Computing the Dynamics of Rotating Bose--Einstein Condensates via Rotating Lagrangian Coordinates

(2013) Weizhu Bao et al.   SIAM JOURNAL ON SCIENTIFIC COMPUTING

Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation

(2012) Weizhu Bao et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Mathematical theory and numerical methods for Bose-Einstein condensation

(2012) Weizhu Bao et al.   Kinetic and Related Models

Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation

(2012) Weizhu Bao et al.   MATHEMATICS OF COMPUTATION

Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations

(2012) Mechthild Thalhammer   SIAM JOURNAL ON NUMERICAL ANALYSIS

Rotating trapped Bose-Einstein condensates

(2009) Alexander L. Fetter   REVIEWS OF MODERN PHYSICS

High-order time-splitting Hermite and Fourier spectral methods

(2008) Mechthild Thalhammer et al.   JOURNAL OF COMPUTATIONAL PHYSICS

High-Order Exponential Operator Splitting Methods for Time-Dependent Schrödinger Equations

(2008) Mechthild Thalhammer   SIAM JOURNAL ON NUMERICAL ANALYSIS