A State Space Error Estimate for POD-DEIM Nonlinear Model Reduction

Authors:
Saifon Chaturantabut;Danny C. Sorensen
Affiliations:
saifonc@math.vt.edu;sorensen@rice.edu
Venue:
SIAM Journal on Numerical Analysis
Year:
2012

Citing 10
Cited 4

Bounds on nonlinear operators in finite-dimensional banach spaces

Numerische Mathematik
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics

SIAM Journal on Numerical Analysis
Ordinary Differential Equations in Theory and Practice

Ordinary Differential Equations in Theory and Practice
A New Look at Proper Orthogonal Decomposition

SIAM Journal on Numerical Analysis
Error Estimation for Reduced-Order Models of Dynamical Systems

SIAM Journal on Numerical Analysis
Error Estimation for Reduced-Order Models of Dynamical Systems

SIAM Review
A posteriori error estimation and basis adaptivity for reduced-basis approximation of nonaffine-parametrized linear elliptic partial differential equations

Journal of Computational Physics
Reduced-basis methods for elliptic equations in sub-domains with a posteriori error bounds and adaptivity

Applied Numerical Mathematics
Nonlinear Model Reduction via Discrete Empirical Interpolation

SIAM Journal on Scientific Computing
A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model

Journal of Computational Physics
The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows

Journal of Computational Physics
A numerical investigation of velocity-pressure reduced order models for incompressible flows

Journal of Computational Physics
Non-linear model reduction for the Navier-Stokes equations using residual DEIM method

Journal of Computational Physics

Quantified Score

Hi-index	0.02

Visualization

Abstract

This paper derives state space error bounds for the solutions of reduced systems constructed using proper orthogonal decomposition (POD) together with the discrete empirical interpolation method (DEIM) recently developed for nonlinear dynamical systems [SIAM J. Sci. Comput., 32 (2010), pp. 2737-2764]. The resulting error estimates are shown to be proportional to the sums of the singular values corresponding to neglected POD basis vectors both in Galerkin projection of the reduced system and in the DEIM approximation of the nonlinear term. The analysis is particularly relevant to ODE systems arising from spatial discretizations of parabolic PDEs. The derivation clearly identifies where the parabolicity is crucial. It also explains how the DEIM approximation error involving the nonlinear term comes into play.