Global energy preserving model reduction for multi-symplectic PDEs
DOI10.1016/j.amc.2022.127483OpenAlexW4293416869WikidataQ114210774 ScholiaQ114210774MaRDI QIDQ2673950
Murat Uzunca, Ayhan Aydin, Bülent Karasözen
Publication date: 21 September 2022
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2203.10933
Hamiltonian PDEproper orthogonal decompositionmodel reductionenergy preservationdiscrete empirical interpolation methodmulti-symplecticity
KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)
Cites Work
- Numerical analysis of AVF methods for three-dimensional time-domain Maxwell's equations
- The multi-symplectic Fourier pseudospectral method for solving two-dimensional Hamiltonian PDEs
- Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs
- Multi-symplectic integration of the Camassa-Holm equation
- Backward error analysis for multi-symplectic integration methods
- Energy preserving model order reduction of the nonlinear Schrödinger equation
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Structure-preserving model reduction for dynamical systems with a first integral
- Dynamical reduced basis methods for Hamiltonian systems
- Two classes of linearly implicit local energy-preserving approach for general multi-symplectic Hamiltonian PDEs
- Symplectic wavelet collocation method for Hamiltonian wave equations
- Decay of the Kolmogorov \(N\)-width for wave problems
- Structure-preserving Galerkin POD reduced-order modeling of Hamiltonian systems
- General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs
- A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions
- Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems
- Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schrödinger Equation
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- Geometric Numerical Integration
- Simulating Hamiltonian Dynamics
- Symplectic Model Reduction of Hamiltonian Systems
- Turbulence and the dynamics of coherent structures. I. Coherent structures
- Structure Preserving Model Reduction of Parametric Hamiltonian Systems
- Structure-preserving reduced basis methods for Poisson systems
- Structure preserving model order reduction of shallow water equations
- Rank-adaptive structure-preserving model order reduction of Hamiltonian systems
- Breaking the Kolmogorov Barrier with Nonlinear Model Reduction
- Linearly Implicit Local and Global Energy-Preserving Methods for PDEs with a Cubic Hamiltonian
- Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
- Symplectic and multisymplectic Lobatto methods for the “good” Boussinesq equation
- Reduced basis methods for time-dependent problems
- Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity
- Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations
- Local structure-preserving algorithms for general multi-symplectic Hamiltonian PDEs