Evolution of Nonlinear Reduced-Order Solutions for PDEs with Conserved Quantities

DOI10.1137/21M1415972zbMath1484.65206arXiv2104.13515OpenAlexW3158004996WikidataQ114074044 ScholiaQ114074044MaRDI QIDQ5028407

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Publication date: 9 February 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.13515

zbMATH Keywords

conservation lawspartial differential equationsmodel order reductionGalerkin projection

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33) Numerical problems in dynamical systems (65P99) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

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Cites Work

• Unnamed Item
• Unnamed Item
• Fundamental limitations of ad hoc linear and quadratic multi-level regression models for physical systems
• Exponential time differencing for stiff systems
• High order accurate vortex methods with explicit velocity kernels
• Reduced-order prediction of rogue waves in two-dimensional deep-water waves
• A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
• Reduced-order precursors of rare events in unidirectional nonlinear water waves
• Model Reduction for Flow Analysis and Control
• Focusing of unidirectional wave groups on deep water: an approximate nonlinear Schrödinger equation-based model
• Integrable, Chaotic, and Turbulent Vortex Motion in Two-Dimensional Flows
• Dynamics of monopolar vortices in a strain flow
• Reduction and reconstruction for self-similar dynamical systems
• Vortex Methods
• Reduced-order description of transient instabilities and computation of finite-time Lyapunov exponents
• Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
• The nonlinear evolution and approximate scaling of directionally spread wave groups on deep water
• A minimization principle for the description of modes associated with finite-time instabilities
• Turbulence, Coherent Structures, Dynamical Systems and Symmetry
• Oceanic Rogue Waves
• The disintegration of wave trains on deep water Part 1. Theory
• The degree of knottedness of tangled vortex lines
• The \(N\)-vortex problem. Analytical techniques

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