An Adaptive Mesh Refinement Scheme for 3D Non-Linear Finite Element Analysis of Magnetostatic Problems

3차원 비선형 정자장 문제의 유한요소 해석을 위한 적응 요소분할 기법

  • 최용권 (충북대학교 대학원 전기공학과) ;
  • 류재섭 (LS산전, 전력연구소) ;
  • 고창섭 (충북대학교 전기전자컴퓨터공학부)
  • Published : 2006.06.01

Abstract

A three dimensional adaptive finite element refinement algorithm is developed for non-linear magnetostatic field problems. In the method, the edge elements are used for finite element formulation, and the local error in each element is estimated from the fact that the tangential components of magnetic field intensity and the normal components of magnetic flux density should be continuous at the interface of the two adjacent elements. Based on the estimated error, the elements which have big error are divided into several elements using bisection method. The effectiveness of the developed algorithm is proved through numerical examples.

Keywords

References

  1. S.Y. Hahn, et al., 'A Posteriori Error Estimate for Adaptive Finite Element Mesh Generation', IEEE Trans. on Magn, Vol .24, No. 1, pp. 315-317. Jan. 1988 https://doi.org/10.1109/20.43920
  2. H. S. Kim, H.K. Jung and S. Y. Hahn, 'A Study on Mesh Refinement for 3-D Adaptive Finite Element Method Using Tetrahedral Element', Trans. on KIEE. Vol. 39, No. 9, pp. 921-927, Sep. 1990
  3. H.S. Kim, S.P. Hong, K. Choi, H.K. Jung and S.Y. Hahn, 'A Three Dimensional Adaptive Finite Element Method for Magnetostatic Problems,' IEEE Trans. On Magnetics, Vol .27, No. 5, pp. 4081-4084, Sep. 1991 https://doi.org/10.1109/20.104998
  4. 김형석, 정현교, 한송엽, '3차원 적응 유한요소법을 위한 사면체 요소세분에 관한 연구', 전기학회 논문지, 제39권 9호, pp. 921-927, 1990년 9월
  5. M. Koizumi, 'A New Element Vector in the Volume Integral Equation Method for Nonlinear Magnetostatics', IEEE Trans. on Magn., Vol. 31, No. 3, May 1995 https://doi.org/10.1109/20.376318
  6. M. Rivara, 'Algorithms for refining triangular grids suitable for adaptive and multi-grid techniques', IJNME, Vol. 20, pp. 745-756, 1984 https://doi.org/10.1002/nme.1620200412
  7. M. L. Barton, Z. J. Cendes, 'New Vector Finite Elements for Three-Dimensional Magnetic Field Computation,' IEEE J. Appl. Phys., Vol. 61, No. 8, 99. 3919, 1987 https://doi.org/10.1063/1.338584
  8. TEAM Workshop: test problem(1~14), (1986-1991)
  9. K. Fujiwara, T. Nakata, 'On the Continuity of the Magnetizing Current Density in 3-D Magnetic Field Analysis with Edge Element', IEEE Trans. on Magn., Vol. 31, May 1995 https://doi.org/10.1109/20.376280
  10. A. Kameari, 'Local force calculation in 3D FEM with edge element', International Journal for Applied Electromagnetics in Materials, vol. 3, pp. 231-240, 1993