eddy currents; error estimation; finite element (FE) method; mesh adaptation
Abstract :
[en] A strategy of mesh adaptation in eddy current finite element modeling is developed from both residual and hierarchical error estimators. Wished distributions of element sizes of adapted meshes are determined from the element-wise local contributions to the estimators and define constraints for the mesh generator. Uniform distributions of the local error are searched.
Research Center/Unit :
Applied and Computational Electromagnetics
Disciplines :
Electrical & electronics engineering
Author, co-author :
Dular, Patrick ; Université de Liège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Applied and Computational Electromagnetics (ACE)
Le Menach, Yvonnick; Université Lille 1 > Laboratory of Electrical Engineering and Power Electronics
Tang, Zuqi; Institut National de Recherche en Informatique et en Automatique Paris-Rocquencourt
Creusé, Emmanuel; Université Lille 1 > Laboratoire Paul Painlevé
Piriou, Francis; Université Lille 1 > Laboratory of Electrical Engineering and Power Electronics
Language :
English
Title :
Finite Element Mesh Adaptation Strategy From Residual and Hierarchical Error Estimators in Eddy Current Problems
Publication date :
March 2015
Journal title :
IEEE Transactions on Magnetics
ISSN :
0018-9464
eISSN :
1941-0069
Publisher :
IEEE, Piscataway, United States - New Jersey
Volume :
51
Issue :
3
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique BELSPO - SPP Politique scientifique - Service Public Fédéral de Programmation Politique scientifique
Z. J. Cendes and D. N. Shenton, "Adaptive mesh refinement in the finite element computation of magnetic fields," IEEE Trans. Magn., vol. 21, no. 5, pp. 1811-1816, Sep. 1985.
O. C. Zienkiewicz and J. Z. Zhu, "A simple error estimator and adaptive procedure for practical engineerng analysis," Int. J. Numer. Methods Eng., vol. 24, no. 2, pp. 337-357, Feb. 1987.
S.-Y. Hahn, C. Calmels, G. Meunier, and J.-L. Coulomb, "A posteriori error estimate for adaptive finite element mesh generation," IEEE Trans. Magn., vol. 24, no. 1, pp. 315-317, Jan. 1988.
P. Fernandes, P. Girdinio, P. Molfino, and M. Repetto, "An enhanced error estimator procedure for finite element field computation with adaptive mesh refinement," IEEE Trans. Magn., vol. 26, no. 5, pp. 2187-2189, Sep. 1990.
J.-F. Remacle, P. Dular, A. Genon, and W. Legros, "A posteriori error estimation and adaptive meshing using error in constitutive relation," IEEE Trans. Magn., vol. 32, no. 3, pp. 1369-1372, May 1996.
R. E. Bank and R. K. Smith, "Mesh smoothing using a posteriori error estimates," SIAM J. Numer. Anal., vol. 34, no. 3, pp. 979-997, Jun. 1997.
J. Z. Zhu and Z. Zhang, "The relationship of some a posteriori estimators," Comput. Methods Appl. Mech. Eng., vol. 176, nos. 1-4, pp. 463-475, Jul. 1999.
S. Dufour, G. Vinsard, B. Laporte, and R. Moretti, "Mesh improvement in 2-D eddy-current problems," IEEE Trans. Magn., vol. 38, no. 2, pp. 377-380, Mar. 2002.
D. Ladas et al., "An energy based approach of electromagnetism applied to adaptive meshing and error criteria," IEEE Trans. Magn., vol. 44, no. 6, pp. 1246-1249, Jun. 2008.
P. Dular, "A posteriori error estimation of finite element solutions via the direct use of higher order hierarchal test functions," IEEE Trans. Magn., vol. 45, no. 3, pp. 1360-1363, Mar. 2009.
Z. Cai and S. Zhang, "Flux recovery and a posteriori error estimators: Conforming elements for scalar elliptic equations," SIAM J. Numer. Anal., vol. 48, no. 2, pp. 578-602, Jan. 2010.
Y. Zhao, X. Zhang, S. L. Ho, and W. N. Fu, "An adaptive mesh method in transient finite element analysis of magnetic field using a novel error estimator," IEEE Trans. Magn., vol. 48, no. 11, pp. 4160-4163, Nov. 2012.
Z. Tang, Y. Le Menach, E. Creuse, S. Nicaise, F. Piriou, and N. Nemitz, "Residual based a posteriori error estimators for harmonic and formulations in eddy current problems," IEEE Trans. Magn., vol. 49, no. 5, pp. 1721-1724, May 2013.
Z. Tang, Y. Le Menach, E. Creuse, S. Nicaise, F. Piriou, and N. Nemitz, "Residual and equilibrated error estimators for magnetostatic problems solved by finite element method," IEEE Trans. Magn., vol. 49, no. 12, pp. 5715-5723, Dec. 2013.
Y. Zhao, S. Niu, S. L. Ho, W. N. Fu, and J. Zhu, "A parameterized mesh generation and refinement method for finite element parameter sweeping analysis of electromagnetic devices," IEEE Trans. Magn., vol. 48, no. 2, pp. 239-242, Feb. 2012.
P. Dular, Z. Tang, Y. Le Ménach, E. Creusé, and F. Piriou, "Comparison of residual and hierarchical finite element error estimators in eddy current problems," IEEE Trans. Magn., vol. 50, no. 2, pp. 501-504, Feb. 2014.
C. Geuzaine and J. F. Remacle, "Gmsh: A three-dimensional finite element mesh generator with built-in pre-and post-processing facilities," Int. J. Numer. Methods Eng., vol. 79, no. 11, pp. 1309-1331, 2009.
