Preprint No. MPIMD/14-19

Title: Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell\'s Equations

Author(s): Martin Hess, Sara Grundel, Peter Benner

Email: hessm@mpi-magdeburg.mpg.de

Date: 2014-11-04

Abstract:

The Reduced Basis Method (RBM) generates low-order models of parametrized partial differential equations (PDEs). These allow for the efficient evaluation of parametrized models in many-query and real-time contexts. We use the RBM to generate low order models of micro scale semiconductor devices under variation of frequency, geometry and material parameters. In particular, we focus on the efficient estimation of the discrete stability constant, used in the Reduced Basis error estimation, which enables to generate low-order models with certified accuracy. A good estimation of this discrete stability constant is a challenging problem for Maxwell\'s equations. We therefore test and compare multiple techniques and discuss their properties in this context.

BibTeX:

@TECHREPORT{MPIMD14-19,
author = {Martin Hess and Sara Grundel and Peter Benner},
title = {Estimating the Inf-Sup Constant in Reduced Basis Methods for Time-Harmonic Maxwell\'s Equations},
number = {MPIMD/14-19},
month = nov,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}


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