Stability Preservation in Stochastic Galerkin Projections of Dynamical Systems

DOI10.1137/17M1142223zbMath1440.65275arXiv1708.00958OpenAlexW2964307396WikidataQ127806112 ScholiaQ127806112MaRDI QIDQ5237171

Florian Augustin, Roland Pulch

Publication date: 17 October 2019

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.00958

zbMATH Keywords

Lyapunov equationasymptotic stabilityorthogonal expansionpolynomial chaosstochastic Galerkin method

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solutions to stochastic differential and integral equations (65C30) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (7)

Stable probability of reduced matrix obtained by Gaussian random projection ⋮ Sensitivity analysis of random linear dynamical systems using quadratic outputs ⋮ Stability preservation in Galerkin-type projection-based model order reduction ⋮ Stability-preserving model order reduction for linear stochastic Galerkin systems ⋮ Sensitivity analysis of random linear differential-algebraic equations using system norms ⋮ 10 Model order reduction in uncertainty quantification ⋮ Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical solution of generalized Lyapunov equations
• Stochastic Galerkin techniques for random ordinary differential equations
• Sensitivity analysis and model order reduction for random linear dynamical systems
• Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations
• Stability preservation in Galerkin-type projection-based model order reduction
• Lyapunov matrix equations in system stability and control.
• Practical bifurcation and stability analysis
• On the convergence of generalized polynomial chaos expansions
• Introduction to Uncertainty Quantification
• Eigenvalues of the Jacobian of a Galerkin-Projected Uncertain ODE System
• Solving Ordinary Differential Equations I
• POLYNOMIAL CHAOS FOR LINEAR DIFFERENTIAL ALGEBRAIC EQUATIONS WITH RANDOM PARAMETERS
• Polynomial chaos for the approximation of uncertainties: Chances and limits
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• Solving Parameter-Dependent Lyapunov Equations Using the Reduced Basis Method with Application to Parametric Model Order Reduction
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Stochastic Galerkin Methods for Analyzing Equilibria of Random Dynamical Systems

This page was built for publication: Stability Preservation in Stochastic Galerkin Projections of Dynamical Systems