Space-Time Galerkin POD with Application in Optimal Control of Semilinear Partial Differential Equations

DOI10.1137/17M1135281zbMath1392.35323arXiv1611.04050OpenAlexW2565391434MaRDI QIDQ5745138

Peter Benner, Manuel Baumann, Jan Heiland

Publication date: 5 June 2018

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

Full work available at URL: https://arxiv.org/abs/1611.04050

zbMATH Keywords

optimal controlmodel reductionnonlinear PDElow-rank Galerkin

Mathematics Subject Classification ID

Control/observation systems governed by partial differential equations (93C20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Discrete approximations in optimal control (49M25) PDEs in connection with control and optimization (35Q93) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

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Windowed least-squares model reduction for dynamical systems ⋮ A surrogate optimization approach for inverse problems: application to turbulent mixed-convection flows ⋮ Operator inference and physics-informed learning of low-dimensional models for incompressible flows ⋮ Solving linear parabolic rough partial differential equations ⋮ Space and chaos‐expansion Galerkin proper orthogonal decomposition low‐order discretization of partial differential equations for uncertainty quantification ⋮ Space--Time Least-Squares Petrov--Galerkin Projection for Nonlinear Model Reduction ⋮ Reduced order optimal control of the convective FitzHugh-Nagumo equations ⋮ A Direct Index 1 DAE Model of Gas Networks ⋮ A note on incremental POD algorithms for continuous time data

Uses Software

• FEniCS
• minpack
• FFC
• CSparse
• spacetime-genpod-burgers
• Nutils

Cites Work

• Unnamed Item
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• Tensor-Structured Galerkin Approximation of Parametric and Stochastic Elliptic PDEs
• Direct Methods for Sparse Linear Systems
• A space-time hp-interpolation-based certified reduced basis method for Burgers' equation

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