Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Two Ways to Treat Time in Reduced Basis Methods Read chapter Read first chapter

2017 | Supplement | Chapter

9. ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics

Authors : Andreas Buhr, Christian Engwer, Mario Ohlberger, Stephan Rave

Published in: Model Reduction of Parametrized Systems

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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 in H(curl).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Offline Error Bounds for the Reduced Basis Method
next chapter Reduced-Order Semi-Implicit Schemes for Fluid-Structure Interaction Problems
Literature
1.
Buhr, A., Engwer, C., Ohlberger, M., Rave, S.: ArbiLoMod, a simulation technique designed for arbitrary local modifications. SIAM J. Sci. Comput. (2017). Accepted
2.
Burgard, S., Sommer, A., Farle, O., Dyczij-Edlinger, R.: Reduced-order models of finite-element systems featuring shape and material parameters. Electromagnetics 34(3–4), 143–160 (2014)CrossRef
3.
Carlberg, K., Bou-Mosleh, C., Farhat, C.: Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations. Int. J. Numer. Methods Eng. 86(2), 155–181 (2011)MathSciNetCrossRefMATH
4.
Chen, Y., Hesthaven, J.S., Maday, Y.: A seamless reduced basis element method for 2D Maxwell’s problem: an introduction. Spectral and High Order Methods for Partial Differential Equations: Selected papers from the ICOSAHOM ’09 Conference, June 22–26, Trondheim, Norway, pp. 141–152. Springer, Berlin (2011)
5.
Chen, Y., Hesthaven, J.S., Maday, Y., Rodríguez, J.: Certified reduced basis methods and output bounds for the harmonic Maxwell’s equations. SIAM J. Sci. Comput. 32(2), 970–996 (2010)MathSciNetCrossRefMATH
6.
Dahmen, W., Plesken, C., Welper,G.: Double greedy algorithms: reduced basis methods for transport dominated problems. ESAIM: Math. Model. Numer. Anal. 48(03), 623–663 (2014)MathSciNetCrossRefMATH
7.
Efendiev, Y., Galvis, J., Hou, T.Y.: Generalized multiscale finite element methods (GMsFEM). J. Comput. Phys. 251, 116–135 (2013)MathSciNetCrossRefMATH
8.
Eftang, J.L., Patera, A.T.: Port reduction in parametrized component static condensation: approximation and a posteriori error estimation. Int. J. Numer. Methods Eng. 96(5), 269–302 (2013)MathSciNetMATH
9.
Fares, M., Hesthaven, J.S., Maday, Y., Stamm, B.: The reduced basis method for the electric field integral equation. J. Comput. Phys. 230(14), 5532–5555 (2011)MathSciNetCrossRefMATH
10.
Hess, M.W., Benner, P.: Fast evaluation of time harmonic Maxwell’s equations using the reduced basis method. IEEE Trans. Microw. Theory Tech. 61(6), 2265–2274 (2013)CrossRef
11.
Iapichino, L., Quarteroni, A., Rozza,G.: A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks. Comput. Methods Appl. Mech. Eng. 221–222, 63–82 (2012)MathSciNetCrossRefMATH
12.
13.
Maier, I., Haasdonk, B.: A Dirichlet-Neumann reduced basis method for homogeneous domain decomposition problems. Appl. Numer. Math. 78, 31–48 (2014)MathSciNetCrossRefMATH
14.
Maxwell, J.C.: On physical lines of force. Lond. Edinb. Dublin Philos. Mag. J. Sci. 21(139), 161–175 (1861)
15.
16.
Monk, P.: Finite Element Methods for Maxwell’s Equations Oxford University Press, Oxford (2003)
17.
18.
Ohlberger, M., Schindler, F.: Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment. SIAM J. Sci. Comput. 37(6), A2865–A2895 (2015)CrossRefMATH
19.
Phuong Huynh, D.B., Knezevic, D.J., Patera, A.T.: A static condensation reduced basis element method: approximation and a posteriori error estimation. ESAIM: Math. Model. Numer. Anal. 47(1), 213–251 (2012)MathSciNetCrossRefMATH
20.
Pomplun, J., Schmidt, F.: Accelerated a posteriori error estimation for the reduced basis method with application to 3d electromagnetic scattering problems. SIAM J. Sci. Comput. 32(2), 498–520 (2010)MathSciNetCrossRefMATH
21.
Strouboulis, T., Babuška, I., Copps, K.: The design and analysis of the generalized finite element method. Comput. Methods Appl. Mech. Eng. 181(1), 43–69 (2000)MathSciNetCrossRefMATH
Metadata
Title
ArbiLoMod: Local Solution Spaces by Random Training in Electrodynamics
Authors
Andreas Buhr
Christian Engwer
Mario Ohlberger
Stephan Rave
Copyright Year
2017
Book
Model Reduction of Parametrized Systems

Print ISBN: 978-3-319-58785-1

Electronic ISBN: 978-3-319-58786-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-58786-8_9

Premium Partner

    Image Credits