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Progress In Electromagnetics Research Letters
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COUPLING PROJECTION DOMAIN DECOMPOSITION METHOD AND MESHLESS COLLOCATION METHOD USING RADIAL BASIS FUNCTIONS IN ELECTROMAGNETICS

By Y. Duan, S.-J. Lai, and T. Huang

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Abstract:
This paper presents an efficient meshless approach for solving electrostatic problems. This novel approach is based on combination of radial basis functions-based meshless unsymmetric collocation method with projection domain decomposition method. Under this new method, we just need to solve a Steklov-Poincare interface equation and the original problem is solved by computing a series of independent sub-problems. An electrostatic problem is used as an example to illustrate the application of the proposed approach. Numerical results that demonstrate the accuracy and efficiency of the method are stated.

Citation:
Y. Duan, S.-J. Lai, and T. Huang, "Coupling Projection Domain Decomposition Method and Meshless Collocation Method Using Radial Basis Functions in Electromagnetics," Progress In Electromagnetics Research Letters, Vol. 5, 1-12, 2008.
doi:10.2528/PIERL08092003

References:
1. Wendland, H., Scattered Data Approximation, Cambridge University Press, 2005.

2. Atluri, S. and T. Zhu, "New concepts in meshless methods," Int. J. Numer. Meth. Eng., Vol. 47, 537-556, 2000.
doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<537::AID-NME783>3.0.CO;2-E

3. Kansa, E. J., "Multlqudrms — A scattered data approximation scheme with apphcations to computational fluiddynamics, II. Solutions to parabolic, hyperbolic and elliptic partial differential equations," Computers Math. Applic., Vol. 19, No. 8/9, 147-161, 1990.
doi:10.1016/0898-1221(90)90271-K

4. Quarteroni, A. and A. Valli, Domain Decomposition Method for Partial Differential Equation, Oxford University Press, England, 1999.

5. Schaback, R., "Convergence of unsymmetric kernal-based meshless collocation methods," SIAM J. Numer. Anal., Vol. 45, No. 1, 333-351, 2007.

6. Li, J. and Y. C. Hon, "Domain decomposition for radial basis meshless method," Numer. Method for Partial Differential Equations, Vol. 20, No. 3, 450-462, 2004.
doi:10.1002/num.10096

7. Babuska, I., U. Banerjee, and J. E. Osborn, "Survey of meshless and generalized finite element methods: A unified approach," Acta. Numer., 1-125, Cambridge University Press, 2003.
doi:10.1017/S0962492902000090

8. Viana, S. A., D. Rodger, and H. C. Lai, "Application of the local radial point interpolation method to solve eddy-current problems," IEEE Trans. Magn., Vol. 42, No. 4, 591-594, 2006.
doi:10.1109/TMAG.2006.871966

9. Ho, S. L., S. Y. Yang, H. C. Wong, and G. Ni, "A meshless collocation method based on radial basis functions and wavelets," IEEE Trans. Magn., Vol. 40, No. 2, 1021-1024, 2004.
doi:10.1109/TMAG.2004.824778

10. Ala, G., E. Francomano, A. Tortaorici, E. Toscano, and F. Viola, "A smoothed particle interpolation scheme for transient electromagnetic simulation," IEEE Trans. Magn., Vol. 42, No. 4, 647-650, 2006.
doi:10.1109/TMAG.2006.871387

11. Angell, A. J. and C. M. Rappaport, "Computational modeling analysis of radar scattering by clothing covered arrays of metallic body-worn explosive devices," Progress In Electromagnetics Research, Vol. 76, 285-298, 2007.
doi:10.2528/PIER07070905

12. Hussein, K. F. A., "Fast computational algoritm for EFIE applied to arbitrarily-shaped conducting surfaces," Progress In Electromagnetics Research, Vol. 68, 339-357, 2007.
doi:10.2528/PIER06122502

13. Sun, J., C.-F. Wang, L.-W. Li, and M.-S. Leong, "Mixed potential spatial domain Green's functions in fast computational form for cylindrically stratified media," Progress In Electromagnetics Research, Vol. 45, 181-199, 2004.
doi:10.2528/PIER03071501

14. Bossavit, A., "Generalized finite differences in computational electromagnetics," Progress In Electromagnetics Research, Vol. 32, 45-64, 2001.
doi:10.2528/PIER00080102

15. Marrone, M., "Computational aspects of the cell method in electrodynamics," Progress In Electromagnetics Research, Vol. 32, 317-356, 2001.
doi:10.2528/PIER00080113

16. Tarhasaari, T. and L. Kettunen, "Topological approach to computational electromagnetism," Progress In Electromagnetics Research, Vol. 32, 189-206, 2001.
doi:10.2528/PIER00080108

17. Gross, P. W. and P. R. Kotiuga, "Finite element-based algorithms to make cuts for magnetic scalar potentials: Topological constraints and computational complexity," Progress In Electromagnetics Research, Vol. 32, 207-245, 2001.
doi:10.2528/PIER00080109

18. Marliani, F. and A. Ciccolella, "Computationally efficient expressions of the dyadic Green’s function for rectangular enclosures," Progress In Electromagnetics Research, Vol. 31, 195-223, 2001.
doi:10.2528/PIER00062901

19. Mukerji, S. K., M. George, M. B. Ramamurthy, and K. Asaduzzaman, "Eddy currents in laminated rectangular cores," Progress In Electromagnetics Research, Vol. 83, 435-445, 2008.
doi:10.2528/PIER08062101

20. Cacciola, M., F. C. Morabito, D. Polimeni, and M. Versaci, "Fuzzy characterization of flawed metallic plates with eddy current tests," Progress In Electromagnetics Research, Vol. 72, 241-252, 2007.
doi:10.2528/PIER07031301

21. Shi, X., F.Wei, Q. Huang, L.Wang, and X.-W. Shi, "Novel binary search algorithm of backtracking for RFID tag anti-collision," Progress In Electromagnetics Research B, Vol. 9, 97-104, 2008.
doi:10.2528/PIERB08070802

22. Kazemi, S., H. R. Hassani, G. Dadashzadeh, and F. G. Gharakhili, "Performance improvement in amplitude synthesis of unequally spaced array using least mean square method," Progress In Electromagnetics Research B, Vol. 1, 135-145, 2008.
doi:10.2528/PIERB07103002

23. Guo, S.-X., Y. Gao, and L.-X. Zhang, "Simulation research on turbo equlization algorithm based on microwave fading channel," Progress In Electromagnetics Research Letters, Vol. 4, 99-107, 2008.

24. Su, D., D.-M. Fu, and D. Yu, "Genetic algorithms and method of moments for the design of PIFAS," Progress In Electromagnetics Research Letters, Vol. 1, 9-18, 2008.
doi:10.2528/PIERL07110603

25. Belytschko, T., Y. Y. Lu, and L. Gu, "Element-free Galerkin methods," International Journal for Numerical Methods in Engineering, Vol. 37, 229-256, 1994.
doi:10.1002/nme.1620370205

26. Hon, Y. C. and R. Schaback, "On unsymmetric collocation by radial basis functions," Appl. Math. Comput., Vol. 119, 177-186, 2001.
doi:10.1016/S0096-3003(99)00255-6

27. Ling, L., R. Opfer, and R. Schaback, "Results on meshless collocation technique," Eng. Anal. Bound. Elem., Vol. 30, No. 4, 247-253, 2006.
doi:10.1016/j.enganabound.2005.08.008

28. Ling, L. and R. Schaback, "Stable and convergent unsymmetric meshless collocation methods," SIAM J. Numer. Anal., Vol. 46, No. 3, 1097-1115, 2008.
doi:10.1137/06067300X


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