Adaptive sampling and modal expansions in pattern-forming systems
DOI10.1007/s10444-021-09870-xzbMath1487.65168OpenAlexW3169732919MaRDI QIDQ2048199
Filippo Terragni, María-Luisa Rapún, José M. Vega
Publication date: 5 August 2021
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10444-021-09870-x
proper orthogonal decompositioncollocation methodsKuramoto-Sivashinsky equationadaptive algorithmscomplex Ginzburg-Landau equationpattern-forming systemsreduced order modelssampling techniques
Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Ginzburg-Landau equations (35Q56)
Cites Work
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- Comparative numerical analysis using reduced-order modeling strategies for nonlinear large-scale systems
- Towards an adaptive POD/SVD surrogate model for aeronautic design
- On the use of POD-based ROMs to analyze bifurcations in some dissipative systems
- Calibrated reduced-order POD-Galerkin system for fluid flow modelling
- Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
- Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction
- Reduced order models based on local POD plus Galerkin projection
- Reduced-order fluid/structure modeling of a complete aircraft configuration
- Enablers for robust POD models
- The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems
- Modal reduction of PDE models by means of snapshot archetypes
- On low-dimensional Galerkin models for fluid flow
- Model reduction of dynamical systems by proper orthogonal decomposition: error bounds and comparison of methods using snapshots from the solution and the time derivatives
- LUPOD: collocation in POD via LU decomposition
- An `empirical interpolation' method: Application to efficient reduced-basis discretization of partial differential equations
- Equation-free/Galerkin-free POD-assisted computation of incompressible flows
- Spontaneous symmetry breaking, self-trapping, and Josephson oscillations
- Convective and absolute instabilities of fluid flows in finite geometry
- A reduced order variational multiscale approach for turbulent flows
- POD model order reduction with space-adapted snapshots for incompressible flows
- Sample selection based on sensitivity analysis in parameterized model order reduction
- A mathematical and numerical study of the sensitivity of a reduced order model by POD (ROM-POD), for a 2D incompressible fluid flow
- A New Selection Operator for the Discrete Empirical Interpolation Method---Improved A Priori Error Bound and Extensions
- Exact solutions for generalized variable-coefficients Ginzburg-Landau equation: Application to Bose-Einstein condensates with multi-body interatomic interactions
- Construction of Bifurcation Diagrams Using POD on the Fly
- Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation
- Online Adaptive Model Reduction for Nonlinear Systems via Low-Rank Updates
- Adaptive POD-based low-dimensional modeling supported by residual estimates
- Nonlinear Model Reduction via Discrete Empirical Interpolation
- The world of the complex Ginzburg-Landau equation
- Local POD Plus Galerkin Projection in the Unsteady Lid-Driven Cavity Problem
- Hyper-reduction of mechanical models involving internal variables
- The Reduced Basis Method for Incompressible Viscous Flow Calculations
- Turbulence and the dynamics of coherent structures. I. Coherent structures
- Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
- Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
- Pattern formation outside of equilibrium
- Localized Discrete Empirical Interpolation Method
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