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2011-06-03
Eigenvalue Analysis of Spherical Resonant Cavity Using Radial Basis Functions
By
Progress In Electromagnetics Research Letters, Vol. 24, 69-76, 2011
Abstract
This paper applies a meshless method based on radial basis function (RBF) collocation to solve three-dimensional scalar Helmholtz equation in rectangular coordinates and analyze the eigenvalues of spherical resonant cavity. The boundary conditions of spherical cavity are deduced. The RBF interpolation method and the collocation procedure are applied to the Helmholtz and boundary condition equations, and their discretization matrix formulations are obtained. The eigenvalues of spherical resonant cavity with natural conformal node distribution are computed by the proposed method. Their results are agreement with the analytic solution.
Citation
Sheng-Jian Lai Bing-Zhong Wang Yong Duan , "Eigenvalue Analysis of Spherical Resonant Cavity Using Radial Basis Functions," Progress In Electromagnetics Research Letters, Vol. 24, 69-76, 2011.
doi:10.2528/PIERL11040904
http://www.jpier.org/PIERL/pier.php?paper=11040904
References

1. Marechal, Y., "Some meshless methods for electromagnetic field computations," IEEE Trans. Magn., Vol. 34, No. 5, 3351-3354, 1998.
doi:10.1109/20.717788

2. Park, G. H., K. Krohne, P. Bai, and E. P. Li, Applications of Meshfree Methods in Electromagnetic, IET. Conf. Publ., 1-2, 2008.

3. Lai, S.-J., B.-Z. Wang, Y. Duan, and , "Meshless radial basis function method for transient electromagnetic computations," IEEE Trans. Magn., Vol. 44, No. 10, 2288-2295, 2008.
doi:10.1109/TMAG.2008.2001796

4. Liu, X.-F., B.-Z. Wang, and S.-J. Lai, "Element-free Galerkin method for transient electromagnetic field simulation," Microwave and Optical Technology Letters, Vol. 50, No. 1, 134-138, 2008.
doi:10.1002/mop.23017

5. Kansa, E. J., "Multiqudrics --- A scattered data approximation scheme with applications to computational fluid-dynamics --- I. Surface approximations and partial derivatives," Computer Math. Appli., Vol. 19, 127-145, 1990.
doi:10.1016/0898-1221(90)90270-T

6. Jiang, P. L., S. Q. Li, and C. H. Chan, "Analysis of elliptical waveguides by a meshless collocation method with the Wendland radial basis funcitons," Microwave and Optical Technology Letters, Vol. 32, No. 2, 162-165, 2002.
doi:10.1002/mop.10119

7. Zhao, G., B. L. Ooi, Y. J. Fan, Y. Q. Zhang, I. Ang, and Y. Gao, "Application of conformal meshless RBF coupled with coordinate transformation for arbitrary waveguide analysis," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 1, 3-14, 2007.
doi:10.1163/156939307779391731

8. Lai, S.-J., B.-Z. Wang, and Y. Duan, "Solving Helmholtz equation by meshless radial basis functions method," Progress In Electromagnetics Research B, Vol. 24, 351-367, 2010.
doi:10.2528/PIERB10062303

9. Yu, J. H. and H. Q. Zhang, "Solving waveguide eigenvalue problem by using radial basis function method," World Automation Congress, WAC 2008, 1-5, 2008.

10. Kaufmann, T., C. Fumeaus, C. Engstrom, and R. Vahldieck, "Meshless eigenvalue analysis for resonant structures based on the radial point interpolation method," APMC 2009, 818-821, 2009.

11. Zhang, K. Q. and D. J. Li, Electromagnetic Theory for Microwaves and Optoelectronics, 2nd Ed., Chapter 5, Springer Press, New York, 2008.