Verification of high-order mixed finite-element solution of transient magnetic diffusion problems

IEEE Transactions on Magnetics

Volumn 42, Issue 1, 2006, Pages 25-39

  Rieben, Robert N ^a   White, Daniel A ^a,b  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b Defense Sciences Engineering Division

Author keywords

Computational electromagnetics; Discrete differential forms; Electromagnetic diffusion; H(Curl) and H(Div) conforming methods; High order methods; Maxwell's equations; Transient eddy currents; Vector finite elements

Indexed keywords

COMPUTATIONAL ELECTROMAGNETICS; DISCRETE DIFFERENTIAL FORMS; ELECTROMAGNETIC DIFFUSION; H(CURL) AND H(DIV) CONFORMING METHODS; HIGH-ORDER METHODS; TRANSIENT EDDY CURRENTS; VECTOR FINITE ELEMENTS;

COMPUTATIONAL METHODS; EDDY CURRENTS; ELECTROMAGNETISM; FINITE ELEMENT METHOD; MAXWELL EQUATIONS; TRANSIENTS; VECTORS;

DIFFUSION;

EID: 30344433309     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMAG.2005.860127     Document Type: Article

References (29)

1. Z. Ren, F. Bouillault, A. Razek, A. Bossavit, and J. C. Verite, "A new hybrid model using electric field formulation for 3d eddy current problems." IEEE Trans. Magn., vol. 26, no. 2, pp. 470-473, Mar. 1990.
2. Z. Ren and A. Razek, "A new technique for solving three-dimensional multiply connected eddy current problems," IEE Proc. A - Sci. Meas. Technol., vol. 137, no. 3, pp. 135-140, 1990.
3. P. Bochev, J. Hu, A. Robinson, and R. Tuminaro, "Toward robust Zpinch simulations: Discretization and fast solvers for magnetic diffusion in heterogenous conductors," Electron. Trans. Numer. Anal., vol. 15, pp. 186-210, 2003.
4. A. Bossavit and J. C. Verite, "The "TRIFOU" code: Solving the 3d eddy current problems by using H as the state variable," IEEE Trans. Magn., vol. MAG-19, no. 6, pp. 2465-2470, Nov. 1983.
5. A. Bossavit. Computational Electromagnetism: Variational Formulation, Complementarity, Edge Elements. New York: Academic, 1998.
6. O. Biro and K. Preis, "On the use of the magnetic vector potential in the finite element analysis of three-dimensional eddy currents," IEEE Trans. Magn., vol. 25, no. 4, pp. 3145-3159, Jul. 1989.
7. O. Biro, K. Preis, W. Renhart, K. Richter, and G. Vrisk, "Performance of different vector potential formulations in solving multiply connected eddy current problems," IEEE Trans. Magn., vol. 26, no. 2, pp. 438-441, Mar. 1990.
8. C. Bryant, C. Emson, and C. Trowbridge, "A comparison of Lorentz gauge formulations in eddy current problems," IEEE Trans. Magn., vol. 26. no. 2, pp. 430-433, Mar. 1990.
9. B. Weis and O. Biro, "On the convergence of transient eddy-curent problems." IEEE Trans. Magn., vol. 40, no. Mar., pp. 957-960, 2004.
10. K. Fujiwara, Y. Okada, T. Nakata, and N. Takahashi, "Improvements in the T-Ω method for 3-D eddy current analysis," IEEE Trans. Magn., vol. 24, no. 1, pp. 94-97, Jan. 1988.
11. H. Whitney, Geometric Integration Theory. Princeton, NJ: Princeton Univ. Press, 1957.
12. J. C. Nédélec, "Mixed finite elements in R3," Numer. Math., vol. 35, pp. 315-341, 1980.
13. _, "A new family of mixed finite elements in R3," Numer. Math., vol. 50, pp. 57-81, 1986.
14. P. A. Raviart and J. M. Thomas, "A mixed finite element method for 2nd order elliptic problems," in Mathematical Aspects of the Finite Element Method, I. Galligani and E. Mayera, Eds. New York: Springer-Verlag, 1977, vol. 606 of Lecture Notes on Mathematics, pp. 293-315.
15. J. Jin. The Finite Element Method in Electromagnetics. New York: Wiley, 1993.
16. Iterative and Self Adaptive Finite-Elements in Electromagnetic Modeling, 1998.
17. P. Castillo, R. Rieben, and D. White, "FEMSTER: An object oriented class library of discrete differential forms," in Proc. 2003 IEEE Int. Antennas and Propagation Symp., vol. 2, Columbus, OH, Jun. 2003, pp. 972-975.
18. M. Ainsworth, "Dispersive properties of high-order Nedelec/edge element approximation of the time-harmonic Maxwell equations," Phil, Trans. R. Soc. Lond., vol. 362, no. 1816, pp. 471-491, 2004.
19. R. Rieben, D. White, and G. Rodrigue, "A high order mixed vector finite element method for solving the time dependent Maxwell equations on unstructured grids," J. Comput. Phys., vol. 204, pp. 490-519, 2005.
20. _, "High order symplectic integration methods for finite element solutions to time dependent Maxwell equations," IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 2190-2195, Aug. 2004.
21. D. Post and L. Votta, "Computational science demands a new paradigm," Physics Today, vol. 58, no. 1, pp. 35-41, Jan. 2005.
22. H. Amman, A. Buffa, and J. C. Nedelec, "A justification of eddy currents for theMaxwell equations," SIAM J. Appl. Math., vol. 60, no. 5, pp. 1805-1823, 2000.
23. W. R. Smythe, Static and Dynamic Electricity. New York: McGraw-Hill, 1968.
24. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media. New York: Pergamon, 1960.
25. H. E. Knoepfel, Magnetic Fields. New York: Wiley, 2000.
26. A. Krawczyk and J. A. Tegopoulos, Numerical Modeling of Eddy Currents. Oxford, U.K.: Oxford University/Clarendon Press, 1993.
27. P. Castillo, J. Koining, R. Rieben, M. Stowell, and D. White, "Discrete differential forms: A novel methodology for robust computational electromagnetics," Lawrence Livermore National Laboratory, Center for Applied Scientific Computing, Tech. Rep. UCRL-ID-151522, Jan. 2003.
28. P. Castillo, R. Rieben, and D. White, "FEMSTER: An object orienetd class library of higher-order discrete differential forms," ACM Trans. Math. Soft., to be published.
29. R. L. Burden and J. D. Faires, Numerical Analysis, 6th ed. Pacific Grove, CA: Brooks/Cole, 1997.