Conformal structure-preserving SVM methods for the nonlinear Schrödinger equation with weakly linear damping term
DOI10.1016/j.apnum.2024.06.024zbMath1546.65086MaRDI QIDQ6593428
Publication date: 26 August 2024
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
optimization modelsupplementary variable methodconformal propertieshigh-order accuracydamped nonlinear Schrödinger equation
Numerical optimization and variational techniques (65K10) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) NLS equations (nonlinear Schrödinger equations) (35Q55) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Time-dependent Schrödinger equations and Dirac equations (35Q41) PDE constrained optimization (numerical aspects) (49M41)
Cites Work
- Unnamed Item
- Unnamed Item
- On global solutions to the initial-boundary value problem for the damped nonlinear Schrödinger equations
- Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
- The scalar auxiliary variable (SAV) approach for gradient flows
- Regularity of the attractor for a weakly damped nonlinear Schrödinger equation in \(\mathbb{R}^2\)
- Almost structure-preserving analysis for weakly linear damping nonlinear Schrödinger equation with periodic perturbation
- Supplementary variable method for structure-preserving approximations to partial differential equations with deduced equations
- Linear high-order energy-preserving schemes for the nonlinear Schrödinger equation with wave operator using the scalar auxiliary variable approach
- Scalar auxiliary variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations
- Arbitrarily high-order linear energy stable schemes for gradient flow models
- Improving the accuracy and consistency of the scalar auxiliary variable (SAV) method with relaxation
- Galerkin finite element method for damped nonlinear Schrödinger equation
- Two novel classes of linear high-order structure-preserving schemes for the generalized nonlinear Schrödinger equation
- A new Lagrange multiplier approach for gradient flows
- Efficient schemes for the damped nonlinear Schrödinger equation in high dimensions
- A revisit of the energy quadratization method with a relaxation technique
- Supplementary variable method for thermodynamically consistent partial differential equations
- Conformal conservation laws and geometric integration for damped Hamiltonian PDEs
- Efficient linear schemes with unconditional energy stability for the phase field elastic bending energy model
- Efficient dissipation-preserving scheme for the damped nonlinear Schrödinger equation in three dimensions
- Self-Focusing in the Damped Nonlinear Schrödinger Equation
- Discontinuous Galerkin and multiscale variational schemes for a coupled damped nonlinear system of Schrödinger equations
- Spectral Methods
- Stability of Runge-Kutta Methods for Trajectory Problems
- Soliton in the damped nonlinear Schrödinger equation
- Numerical Optimization
- An Explicit Unconditionally Stable Numerical Method for Solving Damped Nonlinear Schrödinger Equations with a Focusing Nonlinearity
- Optimal error estimate of a conformal Fourier pseudo‐spectral method for the damped nonlinear Schrödinger equation
- Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
- An applicatin of approximate inertial manifolds to a weakly damped nonlinear schrödinger equation
- High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
- Novel Conformal Structure-Preserving Algorithms for Coupled Damped Nonlinear Schrödinger System
- Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
- Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models
- Geometric Numerical Integration
- Variable mesh difference schemes for solving a nonlinear Schrödinger equation with a linear damping term
This page was built for publication: Conformal structure-preserving SVM methods for the nonlinear Schrödinger equation with weakly linear damping term