Skip to main content
SpringerLink
Log in
Book cover

Numerical Mathematics and Advanced Applications - ENUMATH 2013 pp 437–445Cite as

Output Error Bounds for the Dirichlet-Neumann Reduced Basis Method

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 103))

Abstract

The Dirichlet-Neumann reduced basis method is a model order reduction method for homogeneous domain decomposition of elliptic PDEs on a-priori known geometries. It is based on an iterative scheme with full offline-online decomposition and rigorous a-posteriori error estimates. We show that the primal-dual framework for non-compliant output quantities can be transferred to this method. The results are validated by numerical experiments with a thermal block model.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.B.P. Huynh, D. Knezevic, A.T. Patera, A static condensation reduced basis element method: approximation and a posteriori error estimation. Math. Model. Numer. Anal. 47(1), 213–251 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Iapichino, A. Quarteroni, G. Rozza, 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). doi:10.1016/j.cma.2012.02.005

    Article  MathSciNet  Google Scholar 

  3. Y. Maday, E. Rønquist, A reduced-basis element method. J. Sci. Comput. 17, 447–459 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  4. I. Maier, B. Haasdonk, A Dirichlet-Neumann reduced basis method for homogeneous domain decomposition problems. Appl. Numer. Math. 78, 31–48 (2014). doi:10.1016/j.apnum.2013.12.001

    Article  MATH  MathSciNet  Google Scholar 

  5. C. Prud’homme, D.V. Rovas, K. Veroy, L. Machiels, Y. Maday, A.T. Patera, G. Turinici, Reliable real-time solution of parametrized partial differential equations: reduced-basis output bound methods. J. Fluids Eng. 124, 70–80 (2002)

    Google Scholar 

  6. D. Rovas, Reduced basis output bound methods for parametrized PDE’s. PhD thesis, MIT, 2003

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Immanuel Martini & Bernard Haasdonk

Authors
  1. Immanuel Martini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bernard Haasdonk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Immanuel Martini .

Editor information

Editors and Affiliations

  1. MATHICSE-ANMC, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Assyr Abdulle

  2. SB MATHICSE CMCS, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Simone Deparis

  3. SB MATHICSE ANCHP, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Daniel Kressner

  4. SB MATHICSE CSQI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Fabio Nobile

  5. SB MATHICSE GR-PI, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Marco Picasso

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Martini, I., Haasdonk, B. (2015). Output Error Bounds for the Dirichlet-Neumann Reduced Basis Method. In: Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M. (eds) Numerical Mathematics and Advanced Applications - ENUMATH 2013. Lecture Notes in Computational Science and Engineering, vol 103. Springer, Cham. https://doi.org/10.1007/978-3-319-10705-9_43

Download citation

Publish with us

Policies and ethics

Search

Navigation