Skip to main content
Log in

Boundary element methods for magnetostatic field problems: a critical view

  • Published:
Computing and Visualization in Science

Abstract

For the solution of magnetostatic field problems we discuss and compare several boundary integral formulations with respect to their accuracy, their efficiency, and their robustness. We provide fast boundary element methods which are able to deal with multiple connected computational domains, with large magnetic permeabilities, and with complicated structures with small gaps. The numerical comparison is based on several examples, including a controllable reactor as a real-world problem.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Bossavit A.: A rationale for edge-elements in 3D fields computations. IEEE Trans. Magn. 24, 74–79 (1988)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Costabel M., Stephan E.P.: Boundary integral equations for mixed boundary value problems in polygonal domains and Galerkin approximations. In: Fiszdon, W., Wilmanski, K. (eds) Mathematical Models and Methods in Mechanics., pp. 175–251. Banach Centre Publ. 15, PWN, Warschau (1985)

    Google Scholar 

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

    Article  Google Scholar 

  6. Demkowicz, L., Kurtz, J., Pardo, D., Paszynski, M., Rachowicz, W., Zdunek, A.: Computing with hp-Adaptive Finite Elements, vol. 2. Frontiers: Three-Dimensional Elliptic and Maxwell Problems with Applications. Chapman & Hall/CRC, Boca Raton (2008)

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

  11. Krstajic B., Andjelic Z., Miloijkovic S., Babic S.: Nonlinear 3D magnetostatic field computation by the integral equation method with surface and volume magnetic charges. IEEE Trans. Magn. 28, 1088–1091 (1992)

    Article  Google Scholar 

  12. Kuhn M., Langer U., Schöberl J.: Scientific computing tools for 3D magnetic field problems. In: Whiteman J., R. (eds) The Mathematics of Finite Elements and Applications, X, MAFELAP 1999., pp. 239–258. Elsevier, Oxford (2000)

    Chapter  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  17. Of, G., Steinbach, O., Urthaler, P., Andjelic, Z.: Fast boundary element methods for industrial applications in magnetostatics. In: Langer, U., Schanz, M., Steinbach, O., Wendland, W.L. (eds.) Fast Boundary Element Methods in Engineering and Industrial Applications. Springer, Heidelberg (to appear)

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

    Article  MATH  MathSciNet  Google Scholar 

  19. Rjasanow S., Steinbach O.: The Fast Solution of Boundary Integral Equations. Springer, New York (2007)

    MATH  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  22. Steinbach O.: Numerical Approximation Methods for Elliptic Boundary Value Problems. Springer, New York (2008)

    Book  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  24. Steinbach O., Wendland W.L.: On C. Neumann’s method for second-order elliptic systems in domains with non-smooth boundaries. J. Math. Anal. Appl. 262, 733–748 (2001)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Olaf Steinbach.

Additional information

Communicated by Stefan Sauter.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andjelic, Z., Of, G., Steinbach, O. et al. Boundary element methods for magnetostatic field problems: a critical view. Comput. Visual Sci. 14, 117–130 (2011). https://doi.org/10.1007/s00791-011-0167-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00791-011-0167-3

Keywords

Navigation