Error Control Based Model Reduction for Parameter Optimization of Elliptic Homogenization Problems
Ohlberger M, Schaefer M
Research article in edited proceedings (conference) | Peer reviewedAbstract
In this work we are considered with parameter optimization of elliptic multiscale problems with macroscopic optimization functionals and microscopic material design parameters. An efficient approximation is obtained by the reduced basis approach. A posteriori error estimates for the reduced forward problem are obtained in the periodic homogenization setting, using the so called two scale weak formulation of the multiscale problem. The resulting error indicators allow for an efficient offline/online decomposition and are used for an efficient reduced basis construction, both for the homogenization limit, as well as for the approximation of the corresponding cell problems.
Details about the publication
Book title: Proceedings of the 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations
Status: Published
Release year: 2013
Language in which the publication is written: English
Conference: 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations, Paris, France, undefined
Keywords: parameter optimization; multiscale problem; reduced basis method; model reduction; a posteriori error estimate; two scale convergence
Authors from the University of Münster
| Ohlberger, Mario | Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) Center for Nonlinear Science |
| Schaefer, Michael | Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger) |