Numerical Foundations, Integral Methods and Applications

  • K. R. Richter
  • W. M. Rucker
Part of the EURO Courses: Computer and Information Science book series (EUIS, volume 1)


In this paper the mathematical foundations and the application of various integral formulations based on vector and scalar potentials for the numerical treatment of magnetostatic and eddy current problems with the boundary element method (BEM) are presented. Starting from Maxwell’s equations the basic integral equations are derived by applying Green’s theorem for scalar and vector variables and the definition of the appropriate Green’s functions. In order to apply the BEM the discretization of the boundaries into boundary elements is discussed. This discretization transforms the boundary integral equations into a system of algebraic equations which can be solved by various methods. The boundary element formulations and numerical results of examples for three-dimensional magnetostatic field problems and eddy current problems are presented. It can be seen that there exists a wide range of applications of integral methods and which are alternatives to differential equation methods, e.g. the finite element method.


Boundary Element Boundary Element Method Boundary Integral Equation Iron Core Field Quantity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Harrington, R.F. (1968) Field computation by moment methods, The Macmillan Company, New YorkGoogle Scholar
  2. [2]
    Brebbia, C.A. and Walker S. (1980) Boundary element techniques in engineering, Newnes-Butterworths, London.zbMATHGoogle Scholar
  3. [3]
    Simkin, J. and Trowbridge C.W. (1979) ‘On the use of the total scalar potential in the numerical solution of field problems in electromagnetics’, Int. J. Num. Meth. Eng., vol. 14, 423–440.zbMATHCrossRefGoogle Scholar
  4. [4]
    Rucker, W.M. (1985) ‘Boundary element calculation of magnetostatic field problems using the reduced and total scalar potential’, Proceedings 1st IGTE symposium Graz, 38–46.Google Scholar
  5. [5]
    Kalaichelvan S. and Lavers J.D. (1989) ‘Boundary element methods for eddy current problems’, Topics in Boundary Element Resarch (Ed. C.A. Brebbia), vol. 6, Springer-Verlag, 78–117.Google Scholar
  6. [6]
    Morse, P.M. and Feshbach H. (1953) Methods of Theoretical Physics, McGraw-Hill, New York.zbMATHGoogle Scholar
  7. [7]
    Cheung, Y.K. and Yeo M.F. (1979) A practical introduction to finite element analysis, Pitman, London.Google Scholar
  8. [8]
    Rucker, W.M. and Richter K.R. (1988) ‘Three-dimensional magnetostatic field calculation using boundary element method’, IEEE Transactions on Magnetics, vol. 24, 23–26.CrossRefGoogle Scholar
  9. [9]
    Rucker, W.M. and Richter K.R. (1990) ‘A BEM code for 3-d eddy current calculations’, IEEE Transactions on Magnetics, vol. 26, 462–465.CrossRefGoogle Scholar
  10. [10]
    Turner, L. (Editor) (1988) TEAM Workshops: Testproblems.Google Scholar

Copyright information

© ECSC, EEC, EAEC, Brussels and Luxembourg 1990

Authors and Affiliations

  • K. R. Richter
    • 1
  • W. M. Rucker
    • 1
  1. 1.Institute for Fundamentals and Theory in Electrical EngineeringGraz University of TechnologyGrazAustria

Personalised recommendations