FEMAG: A High Performance Parallel Finite Element Toolbox for Electromagnetic Computations
International Journal of Energy and Power Engineering
Volume 5, Issue 1-1, February 2016, Pages: 57-64
Received: Nov. 9, 2015;
Accepted: Nov. 9, 2015;
Published: Nov. 30, 2015
Views 4896 Downloads 158
Tao Cui, National Center for Mathematics and Interdisciplinary Sciences, State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
Xue Jiang, Department of Mathematics, Beijing University of Posts and Telecommunications, Beijing, China
Weiying Zheng, National Center for Mathematics and Interdisciplinary Sciences, State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
This paper presents a parallel finite element toolbox for computing large electromagnetic devices on unstructured tetrahedral meshes, FEMAG—Fem for ElectroMagnetics on Adaptive Grids. The finite element toolbox deals with unstructured tetrahedral meshes and can solve electromagnetic eddy current problems in both frequency domain and time domain. It adopts high-order edge element methods and refines the mesh adaptively based on reliable and efficient finite element a posteriori error estimates. We demonstrate the competitive performance of FEMAG by extensive numerical experiments, including TEAM (Testing Electromagnetic Analysis Methods) Problem 21 and the simulation for a single-phase power transformer.
FEMAG: A High Performance Parallel Finite Element Toolbox for Electromagnetic Computations, International Journal of Energy and Power Engineering. Special Issue: Numerical Analysis, Material Modeling and Validation for Magnetic Losses in Electromagnetic Devices.
Vol. 5, No. 1-1,
2016, pp. 57-64.
H. Ammari, A. Buffa, and J. Nedelec, “A justification of eddy current model for the Maxwell equations”, SIAM J. Appl. Math., 60 (2000), pp. 1805–1823.
Z. Cheng, N. Takahashi, and B. Forghani, “TEAM Problem 21 Family (V.2009)”, approved by the International Compumag Society. [Online] Available: http://www.compumag.org/jsite/team.
I. Babuska and W. C. Rheinboldt, “Error estimates for adaptive finite element computations,” SIAM J. Numer. Anal., vol. 15, no. 4, pp. 736–754, Aug. 1978.
J. Chen, Z. Chen, T. Cui, and L.-B. Zhang, “An adaptive finite element method for the eddy current model with circuit/field couplings,” SIAM J. Sci. Comput., vol. 32, no. 2, pp. 1020–1042, Mar. 2010.
W. Zheng, Z. Chen, and L. Wang, “An adaptive finite element method for the H–ψ formulation of time-dependent eddy current problems”, Numer. Math., 103 (2006), pp. 667–689.
Z. Chen, L. Wang, and W. Zheng, “An adaptive multilevel method for time–harmonic maxwell equations with singularities,” SIAM J. Sci. Comput., vol. 29, no. 1, pp. 118–138, Jan. 2007.
L.-B. Zhang, “A parallel algorithm for adaptive local refinement of tetrahedral meshes using bisection,” Numer. Math. Theory, Methods, Appl., vol. 2, no. 1, pp. 65–89, 2009.
J.N. Nédélec, “A new family of mixed finite elements in R3”, Numer. Math., vol. 50, no. 1, pp. 57-81, 1986.
R. Hiptmair and J. Xu, Auxiliary Space Preconditioning for Edge Elements, IEEE Trans. Magn., vol. 44, no.6, pp.938-941, 2008.
V. E. Henson and U. M. Yang, “BoomerAMG: A parallel algebraic multigrid solver and preconditioner,” Appl. Numer. Math., vol. 41, no. 1, pp. 155–177, Apr. 2002.
X. Jiang and W. Zheng, “An efficient eddy current model for nonlinear Maxwell equations with laminated conductors”, SIAM J. Appl. Math., 72 (2012), pp. 1021–1040.
W. Zheng and Z. Cheng, “An inner-constrained separation technique for 3D finite element modeling of GO silicon steel laminations”, IEEE Trans. Magn., 12 (2012), pp. 667–689.
X. Jiang and W. Zheng, “Homogenization of quasi-static Maxwell’s equations”, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 12(2014). pp. 152-180.
W. Guo and I. Babuska, The h-p version of the finite element method. Part 2. General results and applications, Comput. Mech. 1 (1986) 203--226.
I. Babuska, B. Andersson, B. Guo, J.M. Melenk, and H.S. Oh, Finite element method for solving problems with singular solutions, J. Comput. Appl. Math. 74 (1996) 51-70.
X. Jiang, L. Zhang, and W. Zheng, Adaptive hp-finite element computations for time-harmonic Maxwell's equations, Comm. Comp. Phys., 13 (2013), pp. 559-582.
W. Mitchell, Optimal multilevel iterative methods for adaptive grids, SIAM J. Sci. Stat. Comput, 13 (1992), pp. 146–167.
I. Kossaczky ́, A recursive approach to local mesh refinement in two and three dimensions, J. Comput. Appl. Math. 55 (1994) 275–288.