Skip to main content
SpringerLink
Log in

An Optimized Schwarz Waveform Relaxation Algorithm for Micro-Magnetics

  • Conference paper
Domain Decomposition Methods in Science and Engineering XVII

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 60))

We present an optimized Schwarz waveform relaxation algorithm for the parallel solution in space-time of the equations of ferro-magnetics in the micromagnetic model. We use Robin transmission conditions, and observe fast convergence of the discretized algorithm. We show numerically the existence of an optimal parameter in the Robin condition, and study its dependence on the various physical and numerical parameters.

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

Access this chapter

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Aharoni. Introduction to the Theory of Ferromagnetism. Oxford Science Publication, 1996.

    Google Scholar 

  2. D. Bennequin, M.J. Gander, and L. Halpern. Optimized Schwarz waveform relaxation methods for convection reaction diffusion problems. Technical Report 24, Institut Galilée, Paris XIII, 2004.

    Google Scholar 

  3. M.J. Gander and L. Halpern. Méthodes de relaxation d’ondes (SWR) pour l’équation de la chaleur en dimension 1. C. R. Math. Acad. Sci. Paris, 336(6):519–524, 2003.

    MATH  MathSciNet  Google Scholar 

  4. M.J. Gander and L. Halpern. Absorbing boundary conditions for the wave equation and parallel computing. Math. Comp., 74(249):153–176, 2004.

    Article  MathSciNet  Google Scholar 

  5. M.J. Gander and L. Halpern. Optimized Schwarz waveform relaxation methods for advection reaction diffusion problems. SIAM J. Numer. Anal., 45(2):666–697, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  6. M.J. Gander, L. Halpern, and F. Nataf. Optimal convergence for overlapping and non-overlapping Schwarz waveform relaxation. In C-H. Lai, P. Bjørstad, M. Cross, and O. Widlund, editors, Eleventh International Conference of Domain Decomposition Methods, pages 27–36. ddm.org, 1999.

    Google Scholar 

  7. M.J. Gander, L. Halpern, and F. Nataf. Optimal Schwarz waveform relaxation for the one dimensional wave equation. SIAM J. Numer. Anal., 41(5):1643–1681, 2003.

    Article  MATH  MathSciNet  Google Scholar 

  8. L. Halpern and S. Labbé. La théorie du micromagnétisme. Modélisation et simulation du comportement des matériaux magnétiques. Matapli, 66:77–92, September 2001.

    Google Scholar 

  9. S. Labbé. Simulation Numérique du Comportement Hyperfréquence des Matériaux Ferromagnétiques. PhD thesis, Université Paris 13, Décembre 1998.

    Google Scholar 

  10. S. Labbé and P.-Y. Bertin. Microwave polarizability of ferrite particles. J. Magnetism and Magnetic Materials, 206:93–105, 1999.

    Article  Google Scholar 

  11. É. Trémolet de Lacheisserie, editor. Magnétisme: Fondements, volume I of Collection Grenoble Sciences. EDP Sciences, 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Section de mathématiques, University of Geneva, Case Postale 64, 1211, Genève 4, Switzerland

    Martin J. Gander & Kévin Santugini-Repiquet

  2. Département de mathématiques, Institut Galilée Université Paris 13, 99 av J-B Clément, 93430, Villetaneuse, France

    Laurence Halpern

  3. Laboratoire de mathématiques Bât 405, Université Paris 11, 91405, Orsay, France

    Stéphane Labbé

Authors
  1. Martin J. Gander
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Laurence Halpern
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Stéphane Labbé
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kévin Santugini-Repiquet
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computational Mathematics, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria

    Ulrich Langer  & Walter Zulehner  & 

  2. Institute of Analysis and Scientific Computing — CMCS, Ecole Polytechnique Fédérale de Lausanne EPFL SB IACS CMCS Bâtiment MA, Station 8, 1015, Lausanne, Switzerland

    Marco Discacciati

  3. Department of Applied Physics and Applied Mathematics, Columbia University, 500 W. 120th Street, MC 4701, 10027, New York, NY, USA

    David E. Keyes

  4. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012-1185, USA

    Olof B. Widlund

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Gander, M.J., Halpern, L., Labbé, S., Santugini-Repiquet, K. (2008). An Optimized Schwarz Waveform Relaxation Algorithm for Micro-Magnetics. In: Langer, U., Discacciati, M., Keyes, D.E., Widlund, O.B., Zulehner, W. (eds) Domain Decomposition Methods in Science and Engineering XVII. Lecture Notes in Computational Science and Engineering, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75199-1_22

Download citation

Publish with us

Policies and ethics

Search

Navigation