Generalized finite-element method for magnetized nanoparticles

IEEE Transactions on Magnetics

Volumn 39, Issue 3 I, 2003, Pages 1436-1439

  Plaks, Alexander ^a   Tsukerman, Igor ^b   Friedman, Gary ^c   Yellen, Benjamin ^c  

^a TechnoCom Corporation   (United States)

^b The University of Akron   (United States)

^c Drexel University   (United States)

Author keywords

Generalized finite element method (GFEM); Magnetized particles; Nanotechnology; Partition of unit (PU)

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; MAGNETIZATION; NANOTECHNOLOGY; SELF ASSEMBLY;

GENERALIZED FINITE ELEMENT METHOD; MAGNETIZED PARTICLES; PARTITION OF UNITY;

NANOSTRUCTURED MATERIALS;

EID: 0037844439     PISSN: 00189464     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMAG.2003.810408     Document Type: Article

References (21)

1. B. Yellen, G. Friedman, and A. Feinerman, "Analysis of interactions for magnetic particles assembling on magnetic templates," J. Appl. Phys., vol. 91, no. 10, pp. 8552-8554, 2002.
2. J. M. Melenk and I. Babuška, "The partition of unity finite element method: Basic theory and applications," Comput. Methods Appl. Mech. Eng., vol. 139, pp. 289-314, 1996.
3. I. Babuška and J. M. Melenk, "The partition of unity method," Int. J. Numer. Methods Eng., vol. 40, no. 4, pp. 727-758, 1997.
4. C. A. Duarte, I. Babuška, and J. T. Oden, "Generalized finite element methods for three-dimensional structural mechanics problems," Comput. Struct., vol. 77, no. 2, pp. 215-232, 2000.
5. T. Strouboulis, I. Babuška, and K. L. Copps, "The design and analysis of the generalized finite element method," Comput. Methods Appl. Mech. Eng., vol. 181, no. 1-3, pp. 43-69, 2000.
6. T. Strouboulis, K. Copps, and I. Babuska, "The generalized finite element method," Comput. Methods Appl. Mech. Eng., vol. 190, no. 32-33, pp. 4081-4193, 2001.
7. L. Proekt and I. Tsukerman, "Method of overlapping patches for electromagnetic computation," IEEE Trans. Magn., vol. 38, pp. 741-744, Mar. 2002.
8. I. Tsukerman and L. B. Proekt, "Generalized scalar and vector elements for electromagnetic computation," in Proc. 11th Int. Symp. Theoretical Electrical Engineering, Linz, Austria, Aug. 2001.
9. L. Proekt, S. Yuferev, I. Tsukerman, and N. Ida, "Method of overlapping patches for electromagnetic computation near imperfectly conducting cusps and edges," IEEE Trans. Magn., vol. 38, pp. 649-652, Mar. 2002.
10. T. Belytschko, Y. Krongauz, D. Organ, M. Fleming, and P. Krysl, "Meshless methods: An overview and recent developments," Comput. Methods Appl. Mech. Eng., vol. 139, no. 1-4, pp. 3-47, 1996.
11. Y. Maréchal, "Some meshless methods for electromagnetic field computations," IEEE Trans. Magn., vol. 34, pp. 3351-3354, Sept. 1998.
12. Y. Maréchal, J. L. Coulomb, G. Meunier, and G. Touzot, "Use of the diffuse approximation method for electromagnetic field computation," IEEE Trans. Magn., vol. 30, pp. 3558-3561, Sept. 1994.
13. I. A. Tsukerman, "Approximation of conservative fields and the element 'edge shape matrix'," IEEE Trans. Magn., vol. 34, pp. 3248-3251, Sept. 1998.
14. I. A. Tsukerman and A. Plaks, "Comparison of accuracy criteria for approximation of conservative fields on tetrahedra," IEEE Trans. Magn., vol. 34, pp. 3252-3255, Sept. 1998.
15. I. A. Tsukerman, "Overlapping finite elements for problems with movement," IEEE Trans. Magn., vol. 28, pp. 2247-2249, Sept. 1992.
16. ____, "Accurate computation of 'ripple solutions' on moving finite element meshes," IEEE Trans. Magn., vol. 31, pp. 1472-1475, May 1995.
17. W. Müller, "Comparison of different methods of force calculation," IEEE Trans. Magn., vol. 26, pp. 1058-1061, Mar. 1990.
18. L. Greengard, V. Rokhlin, and H. Cheng, "A fast adaptive maultipole algorithm in three dimensions," J. Comput. Phys., vol. 155, no. 2, pp. 468-498, 1999.
19. I. Tsukerman and A. Plaks, "Hierarchical basis multilevel preconditioners for 3-D magnetostatic problems," IEEE Trans. Magn., vol. 35, pp. 1143-1146, May 1999.
20. I. Babuška, G. Caloz, and J. E. Osborn, "Special finite-element methods for a class of 2nd-order elliptic problems with rough coefficients," SIAM J. Num. Anal., vol. 31, no. 4, pp. 945-981, 1994.
21. I. Tsukerman, "Finite element difference schemes for electro- and magnetostatics," in Proc. Compumag, 2003, to be published.