High-Order Mass- and Energy-Conserving Methods for the Nonlinear Schrödinger Equation
DOI10.1137/22m152178xMaRDI QIDQ6154206
Genming Bai, Buyang Li, Jiashun Hu
Publication date: 19 March 2024
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
mass conservationfinite element methodnonlinear Schrödinger equationenergy conservationhigh-order time discretizationGauss collocationpost-processing correction
Numerical computation of solutions to systems of equations (65H10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Unnamed Item
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- A new error analysis of Crank-Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation
- Splitting integrators for nonlinear Schrödinger equations over long times
- Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate
- On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation
- The nonlinear Schrödinger equation. Self-focusing and wave collapse
- The scalar auxiliary variable (SAV) approach for gradient flows
- Ground-state solution of Bose--Einstein condensate by directly minimizing the energy functional
- Mathematical theory and numerical methods for Bose-Einstein condensation
- Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation
- Unconditional convergence and optimal error estimates of the Euler semi-implicit scheme for a generalized nonlinear Schrödinger equation
- On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
- Spectral Methods
- Water waves, nonlinear Schrödinger equations and their solutions
- On splitting methods for Schrödinger-Poisson and cubic nonlinear Schrödinger equations
- Methods for the Numerical Solution of the Nonlinear Schroedinger Equation
- Optimal H1 Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
- A Space-Time Finite Element Method for the Nonlinear Schrödinger Equation: The Continuous Galerkin Method
- A space-time finite element method for the nonlinear Schrödinger equation: the discontinuous Galerkin method
- Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow
- A Relaxation Scheme for the Nonlinear Schrödinger Equation
- Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schrödinger Equations
- Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation
- Energy-preserving methods for nonlinear Schrödinger equations
- High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
- Superconvergence of time invariants for the Gross–Pitaevskii equation
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Crank–Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials
- On accuracy of the mass-preserving DG method to multi-dimensional Schrödinger equations
- A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas
