Skip to main content
SpringerLink
Log in

Fast Boundary Element Methods for Industrial Applications in Magnetostatics

  • Chapter
  • First Online:
Fast Boundary Element Methods in Engineering and Industrial Applications

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 63))

Abstract

For the solution of magnetostatic field problems with industrial applications we consider several boundary integral formulations for a scalar potential ansatz. The presented fast boundary element methods are capable to deal with simply and multiple connected domains, large jumps in the magnetic permeabilities, and real–world examples. We compare the formulations on the basis of several numerical examples taking into account accuracy, efficiency, and robustness.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andjelic, Z., Of, G., Steinbach, O., Urthaler, P.: Boundary element methods for magnetostatic field problems: A critical view. Comput. Visual Sci. 14, 117–130 (2011)

    Article  Google Scholar 

  2. Bebendorf, M., Rjasanow, S.: Adaptive low–rank approximation of collocation matrices. Computing 70(1), 1–24 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Beuchler, S., Eibner, T., Langer, U.: Primal and dual interface concentrated iterative substructuring methods. SIAM J. Numer. Anal. 46, 2818–2842 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bossavit, A.: A rationale for ‘edge–elements’ in 3-d fields computations. IEEE Trans. Magn. 24(1), 74–79 (1988)

    Article  Google Scholar 

  5. Buchau, A., Rucker, W.M., Rain, O., Rischmüller, V., Kurz, S., Rjasanow, S.: Comparison between different approaches for fast and efficient 3-D BEM computations. IEEE Trans. Magn. 39(3), 1107–1110 (2003)

    Article  Google Scholar 

  6. Colton, D.L., Kress, R.: Integral equation methods in scattering theory. Pure and Applied Mathematics. John Wiley & Sons Inc., New York (1983)

    MATH  Google Scholar 

  7. Costabel, M., Stephan, E.P.: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximation. In: Mathematical Models and Methods in Mechanics, vol. 15, pp. 175–251. Banach Center Publ., PWN, Warsaw (1985)

    Google Scholar 

  8. Coulomb, J.L.: Finite elements three dimensional magnetic field computation. IEEE Trans. Magn. 17(6), 3241–3246 (1981)

    Article  Google Scholar 

  9. Demkowicz, L., Kurtz, J., Pardo, D., Paszynski, M., Rachowicz, W., Zdunek, A.: Computing with hp–adaptive finite elements. Frontiers: three–dimensional elliptic and Maxwell problems with applications, vol. 2. Chapman & Hall/CRC, Boca Raton (2008)

    MATH  Google Scholar 

  10. Erichsen, S., Sauter, S.A.: Efficient automatic quadrature in 3-D Galerkin BEM. Comput. Methods Appl. Mech. Eng. 157(3-4), 215–224 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Forster, H., Schrefl, T., Dittrich, R., Scholz, W., Fidler, J.: Fast boundary methods for magnetostatic interactions in micromagnetics. IEEE Trans. Magn. 39(5), 2513–2515 (2003)

    Article  Google Scholar 

  12. Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73, 325–348 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hafla, W., Groh, F., Buchau, A., Rucker, W.M.: Magnetostatic field computations by an integral equation method using a difference field concept and the fast multipole method. In: Proceedings of the 10th International IGTE Symposium on Numerical Field Calculation in Electrical Engineering, pp. 262–266 (2002)

    Google Scholar 

  14. Hofreither, C., Langer, U., Pechstein, C.: Analysis of a non–standard finite element method based on boundary integral operators. Electr. Trans. Numer. Anal. 436, 413–436 (2010)

    MathSciNet  Google Scholar 

  15. Hsiao, G.C., Wendland, W.L.: Boundary integral equations. Applied Mathematical Sciences, vol. 164. Springer, Berlin (2008)

    Book  MATH  Google Scholar 

  16. Ishibashi, K., Andjelic, Z.: Nonlinear magnetostatic BEM formulation using one unknown double layer charge. In: Proceedings of the 14th International IGTE Symposium 2010 (2010)

    Google Scholar 

  17. Khoromskij, B.N., Melenk, J.M.: Boundary concentrated finite element methods. SIAM J. Numer. Anal. 41, 1–36 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  18. Khoromskij, B.N., Wittum, G.: Numerical Solution of Elliptic Differential Equations by Reduction to the Interface. LNCSE, vol. 36. Springer, Heidelberg (2004)

    Google Scholar 

  19. Krstajic, B., Andelic, Z., Milojkovic, S., Babic, S., Salon, S.: Nonlinear 3D magnetostatic field calculation by the integral equation method with surface and volume magnetic charges. IEEE Trans. Magn. 28(2), 1088–1091 (1992)

    Article  Google Scholar 

  20. Kuhn, M., Langer, U., Schöberl, J.: Scientific computing tools for 3D magnetic field problems. In: The Mathematics of Finite Elements and Applications, pp. 239–258. Elsevier (2000)

    Google Scholar 

  21. Lindholm, D.: Notes on boundary integral equations for three–dimensional magnetostatics. IEEE Trans. Magn. 16(6), 1409–1413 (1980)

    Article  Google Scholar 

  22. Magele, C., Stogner, H., Preis, K.: Comparison of different finite element formulations for 3D magnetostatic problems. IEEE Trans. Magn. 24(1), 31–34 (1988)

    Article  Google Scholar 

  23. Mayergoyz, I., Chari, M., D’Angelo, J.: A new scalar potential formulation for three–dimensional magnetostatic problems. IEEE Trans. Magn. 23(6), 3889–3894 (1987)

    Article  Google Scholar 

  24. Mayergoyz, I.D., Andrei, P., Dimian, M.: Nonlinear magnetostatic calculations based on fast multipole method. IEEE Trans. Magn. 39(3), 1103–1106 (2003)

    Article  Google Scholar 

  25. McLean, W.: Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  26. Of, G., Steinbach, O., Wendland, W.L.: The fast multipole method for the symmetric boundary integral formulation. IMA J. Numer. Anal. 26(2), 272–296 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  27. von Petersdorff, T., Schwab, C.: Wavelet approximations for first kind boundary integral equations on polygons. Numer. Math. 74(4), 479–516 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  28. Radon, J.: Zur mechanischen Kubataur. Monatshefte Math. 52, 286–300 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  29. Rjasanow, S., Steinbach, O.: The fast solution of boundary integral equations. Mathematical and Analytical Techniques with Applications to Engineering. Springer, New York (2007)

    MATH  Google Scholar 

  30. Rucker, W.M., Richter, K.R.: Three–dimensional magnetostatic field calculation using boundary element method. IEEE Trans. Magn. 24(1), 23–26 (1988)

    Article  Google Scholar 

  31. Sauter, S.A., Schwab, C.: Boundary Element Methods. Springer Series in Computational Mathematics, vol. 39. Springer, Heidelberg (2011)

    Book  MATH  Google Scholar 

  32. Steinbach, O.: Artificial multilevel boundary element preconditioners. Proc. Appl. Math. Mech. 3, 539–542 (2003)

    Article  MathSciNet  Google Scholar 

  33. Steinbach, O.: Stability estimates for hybrid coupled domain decomposition methods. LNM, vol. 1809. Springer, Berlin (2003)

    MATH  Google Scholar 

  34. Steinbach, O.: Numerical approximation methods for elliptic boundary value problems. Finite and boundary elements. Springer, New York (2008)

    Book  MATH  Google Scholar 

  35. Steinbach, O., Wendland, W.L.: The construction of some efficient preconditioners in the boundary element method. Adv. Comput. Math. 9(1-2), 191–216 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Corporate Research, ABB Switzerland Ltd., 5405, Baden–Dättwil, Switzerland

    Zoran Andjelic

  2. Institut für Numerische Mathematik, TU Graz, Steyrergasse 30, 8010, Graz, Austria

    Günther Of, Olaf Steinbach & Peter Urthaler

Authors
  1. Zoran Andjelic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Günther Of
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Olaf Steinbach
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter Urthaler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zoran Andjelic .

Editor information

Editors and Affiliations

  1. Inst. Numerische Mathematik, Universität Linz, Altenbergerstr. 69, Linz, 4040, Austria

    Ulrich Langer

  2. Inst. Allgemeine Mechanik, TU Graz, Technikerstr. 4, Graz, 8010, Austria

    Martin Schanz

  3. Institut für Numerische Mathematik, Technische Universität Graz, Steyrergasse 30, Graz, 8010, Austria

    Olaf Steinbach

  4. Institut für Angewandte Analysis, und Numerische Simulation, Universität Stuttgart, Pfaffenwaldring 57, Stuttgart, 70569, Germany

    Wolfgang L. Wendland

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Andjelic, Z., Of, G., Steinbach, O., Urthaler, P. (2012). Fast Boundary Element Methods for Industrial Applications in Magnetostatics. In: Langer, U., Schanz, M., Steinbach, O., Wendland, W. (eds) Fast Boundary Element Methods in Engineering and Industrial Applications. Lecture Notes in Applied and Computational Mechanics, vol 63. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25670-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25670-7_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25669-1

  • Online ISBN: 978-3-642-25670-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation