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ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics

Buhr A, Engwer C, Ohlberger M, Rave S

Research article (book contribution) | Peer reviewed

Abstract

The simulation method ArbiLoMod (Buhr et al., SIAM J. Sci. Comput. 2017, accepted) has the goal of providing users of Finite Element based simulation software with quick re-simulation after localized changes to the model under consideration. It generates a Reduced Order Model (ROM) for the full model without ever solving the full model. To this end, a localized variant of the Reduced Basis method is employed, solving only small localized problems in the generation of the reduced basis. The key to quick re-simulation lies in recycling most of the localized basis vectors after a localized model change. In this publication, ArbiLoMod’s local training algorithm is analyzed numerically for the non-coercive problem of time harmonic Maxwell’s equations in 2D, formulated inH(curl).

Details about the publication

Publisher: Benner P., Ohlberger M., Patera A., Rozza G., Urban K.
Book title: Model Reduction of Parametrized Systems (Volume 2016)
Page range: 137-148
Publishing company: Springer International Publishing
Place of publication: Cham
Title of series: MS&A (Modeling, Simulation and Applications)
Volume of series: 17
Status: Published
Release year: 2017
Language in which the publication is written: English
ISBN: 978-3-319-58785-1
DOI: 10.1007/978-3-319-58786-8_9

Authors from the University of Münster

Buhr, Andreas
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Engwer, Christian
Professorship for Applications of Partial Differential Equations
Center for Nonlinear Science
Ohlberger, Mario
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Center for Nonlinear Science
Center for Multiscale Theory and Computation
Rave, Stephan
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)