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Improving Efficiency of the Secondary Sources Method for Modeling of the Three-Dimensional Electromagnetic Field of Eddy Currents

By Dmitriy M. Filippov and Alexandr A. Shuyskyy
Progress In Electromagnetics Research M, Vol. 78, 19-27, 2019


A mathematical model is constructed for calculating a three-dimensional quasistationary electromagnetic field in a piecewise-homogeneous medium containing massive conductors which is excited by a variable magnetic field. The field is varying in time according to an arbitrary law. It is proposed to use the integral relation instead of the boundary condition written at a point, which allows one to get away from the problem of collocation points and at the same time increase the computational efficiency of the numerical model. The magnetic field is calculated for the case of the excitation of eddy currents in a conducting sample containing a cut of finite size. The results obtained are confirmed by natural experiments.


Dmitriy M. Filippov and Alexandr A. Shuyskyy, "Improving Efficiency of the Secondary Sources Method for Modeling of the Three-Dimensional Electromagnetic Field of Eddy Currents," Progress In Electromagnetics Research M, Vol. 78, 19-27, 2019.


    1. Irazu, L. and M. J. Elejabarrieta, "Analysis and numerical modelling of eddy current damper for vibration problems," Journal of Sound and Vibration, Vol. 426, 75-89, July 2018.

    2. Kuczmann, M., "Numerical analysis of eddy current field in laminated media," Pollack Periodica, Vol. 13, No. 2, 3-14, 2018.

    3. Maraspin, F., P. Bevilacqua, and P. Rem, "Modelling the throw of metals and nonmetals in eddy current separations," International Journal of Mineral Processing, Vol. 73, No. 1, 1-11, 2004.

    4. Aubert, G., J.-F. Jacquinot, and D. Sakellariou, "Eddy current effects in plain and hollow cylinders spinning inside homogeneous magnetic fields: Application to magnetic resonance," Journal of Chemical Physics, Vol. 137, No. 15, 1-14, 2012.

    5. Yatchev, I., "Numerical eddy current modelling," Proc. XLVII ETRAN Conference, Vol. 2, 235-241, Herceg Novi, June 8–13, 2003.

    6. Heller, C. J., Handbook of Nondestructive Evaluation, McGraw-Hill, New York, 2001.

    7. Mohanty, I., R. Nagendran, A. V. T. Arasu, R. Baskaran, and A. Mani, "Correlation of defect depth with diffusion time of eddy currents for the defects in conducting materials by using transient eddy current NDE," Measurement Science and Technology, Vol. 29, No. 10, 215 pages, 2018, https://doi.org/10.1088/1361-6501/aad613.

    8. Zhilichev, Y., "Solutions of eddy-current problems in a finite length cylinder by separation of variables," Progress In Electromagnetics Research B, Vol. 81, 81-100, 2018.

    9. Nagel, J. R., "Induced eddy currents in simple conductive geometries," IEEE Antennas and Propagation Magazine, Vol. 60, No. 1, 81-88, 2018.

    10. Nagel, J. R., "Fast finite-difference calculation of eddy currents in thin metal sheets," Applied Computational Electromagnetics Society Journal, Vol. 33, No. 6, 575-584, 2018.

    11. Pipis, K., A. Skarlatos, T. Theodoulidis, and D. Lesselier, "ECT-signal calculation of cracks near fastener holes using an integral equation formalism with dedicated Green’s kernel," IEEE Transactions on Magnetics, Vol. 52, No. 4, 1-8, April 2016.

    12. Bowler, J. R., "Eddy-current interaction with an ideal crack. I. The forward problem," Journal of Applied Physics, Vol. 75, No. 12, 8128-8137, 1994.

    13. Bettini, P. and R. Specogna, "A boundary integral method for computing eddy currents in thin conductors of arbitrary topology," IEEE Transactions on Magnetics, Vol. 51, No. 3, 1-4, March 2015.

    14. Bettini, P., M. F. Palumbo, and R. Specogna, "A boundary element method for eddy-current problems in fusion devices," Fusion Engineering and Design, Vol. 96-97, 620-623, 2015.

    15. Mayergoyz, I. D., "Boundary integral equations of minimum order for the calculation of three-dimensional eddy current problems," IEEE Transactions on Magnetics, Vol. 18, No. 2, 536-539, March 1982.

    16. Filippov, D. M., G. P. Kozik, A. V. Fursenko, and V. N. Fedorovsky, "The secondary sources method analysis and experimental modeling of the permanent magnet eddy currents suspansion," Proc. of 2nd International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM), 1-4, 2016.

    17. Halfla, W., A. Buchau, F. Groh, and W. M. Rucker, "Efficient integral equation method for the solution of 3-D magnetostatic problems," IEEE Transactions on Magnetics, Vol. 41, No. 5, 1408-1411, May 2005.

    18. Adelman, R., N. A. Gumerov, and R. Duraiswami, "Computation of galerkin double surface integrals in the 3-D boundary element method," IEEE Transactions on Antennas and Propagation, Vol. 64, No. 6, 2389-2400, June 2016.

    19. Stenroos, M. and J. Haueisen, "Boundary element computations in the forward and inverse problems of electrocardiography comparison of collocation and Galerkin Weightings," IEEE Transactions on Biomedical Engineering, Vol. 55, No. 9, 2124-2133, September 2008.

    20. Hantila, F. I., "Modelling eddy currents in the shields," COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 28, No. 4, 2009.

    21. Shen, J., Z. Andjelic, and B. Schaub, "A hybrid single and dial simple layer bondary integral equation formulation for 3-D eddy currents," IEEE Transactions on Magnetics, Vol. 34, No. 5, 2636-2639, September 1998.

    22. Ishibashi, K., Z. Andjelic, and D. Pusch, "Nonlinear eddy current analysis by BEM utilizing adaptive equation technique," IEEE Transactions on Magnetics, Vol. 45, No. 3, 1020-1023, March 2000.

    23. Berzhansky, V. N., D. M. Filippov, and N. V. Lugovskoy, "Magneto-optical visualization of eddy current magnetic fields," Physics Procedia, Vol. 82, 27-31, 2016.