Adaptive POD basis computation for parametrized nonlinear systems using optimal snapshot location

DOI10.1007/s10589-014-9646-zzbMath1302.49040OpenAlexW2003455389MaRDI QIDQ457232

Stefan Volkwein, Oliver Lass

Publication date: 26 September 2014

Published in: Computational Optimization and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10589-014-9646-z

zbMATH Keywords

optimal controloptimality conditionsproper orthogonal decompositionHelmholtz equationreduced-order modeling

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Newton-type methods (49M15) Methods of quasi-Newton type (90C53) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Decomposition methods (49M27)

Related Items

Model order reduction for nonlinear Schrödinger equation, Certified reduced order method for the parametrized Allen-Cahn equation, A fully adaptive nonintrusive reduced-order modelling approach for parametrized time-dependent problems, A New Algorithm of Proper Generalized Decomposition for Parametric Symmetric Elliptic Problems

Uses Software

• rbMIT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Admittance identification from point-wise sound pressure measurements using reduced-order modelling
• Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
• A reduced-order method for simulation and control of fluid flows
• An Adaptive POD Approximation Method for the Control of Advection-Diffusion Equations
• Efficient reduced-basis treatment of nonaffine and nonlinear partial differential equations
• Galerkin proper orthogonal decomposition methods for parameter dependent elliptic systems
• Optimal snapshot location for computing POD basis functions
• First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems
• Proper orthogonal decomposition for flow calculations and optimal control in a horizontal CVD reactor
• Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
• Turbulence, Coherent Structures, Dynamical Systems and Symmetry