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Analytical Solution of Helmholtz Equation in Anisotropic and Nonhomogeneous Region

Analytical Solution of Helmholtz Equation in Anisotropic and Nonhomogeneous Region
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摘要 The analytical solution of Helmholtz equation for magnetic vector potential in anisotropic and nonhomogeneous region is presented. The solution is built of a combination of both Bessel and power functions. There are developed two examples that proof the accuracy of the proposed analytical solution. First example is showing the electromagnetic field analysis in slot of ferromagnetic rotor of electrical induction machine. The second example approaches electromagnetic field wave in resonator of the form of rectangular cavity The analytical solution presented is treated as an exact one and is being compared with the numerical solution, e.g., given by finite element method. The analytical solution can be used as a benchmark test for numerical algorithms,
出处 《Journal of Energy and Power Engineering》 2014年第7期1265-1271,共7页 能源与动力工程(美国大卫英文)
关键词 Helmholtz equation anisotropic and nonhomogeneous region analytical and numerical solutions. 亥姆霍兹方程 各向异性 解析解 非均质 电磁场分析 矩形空腔 有限元法 数值算法
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参考文献6

  • 1Binns, K. J., Lawrenson, P. J., and Trowbridge, C. W. 1992. The Analytical and Numerical Solution of Electric and Magnetic Fields. New York: John Wiley & Sons.
  • 2Jackson, J. D. 1999. Classical Electrodynamics. New York: John Wiley.
  • 3Frankl, D. R. 1986. Electromagnetic Theory, New Jersey: Englewood Cliffs.
  • 4Gradsztajn, I. S., and Ryzik, I. M. 1962. Tables of Integrals, Sums, Series and Items. Moscow: Academic Press.
  • 5Kammel, G., and Franek, H. 1990. Einfuehrung in die Methode der finiten Elemente. 2nd. Edition. Leipzig: Fachbuchverlag.
  • 6Spatek, D. 2009. "Spherical Induction Motor with Anisotropic rotor--Analytical Solutions for Electromagnetic Field Distribution, Electromagnetic Torque and Power Losses." International Compumag Society. T.E.A.M. Testing Electromagnetic Analysis Method. problem no. 34. Accessed July, 2009. http://www.compumag.org/j site/team.html.

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