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Progress In Electromagnetics Research
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APPLYING DIVERGENCE-FREE CONDITION IN SOLVING THE VOLUME INTEGRAL EQUATION

By M. Li and W. C. Chew

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Abstract:
Applying divergence-free condition to volume integral equation solver will be discussed. Three schemes are available: basis reduction scheme, minimal complete volume loop basis set and expanded volume loop basis set. All of them will generate smaller matrix equations than the SWG basis. The first two schemes generate poorly-conditioned matrices that are hard to solve by iterative solvers. The expanded loop basis set is easier to solve iteratively in spite of the existence of a null space in the matrix. Moreover, the construction of the expanded loop basis set is much easier than the other two schemes.

Citation: (See works that cites this article)
M. Li and W. C. Chew, "Applying Divergence-Free Condition in Solving the Volume Integral Equation," Progress In Electromagnetics Research, Vol. 57, 311-333, 2006.
doi:10.2528/PIER05061303
http://www.jpier.org/PIER/pier.php?paper=0506133

References:
1. Born, M. and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed., Cambridge University Press, Cambridge [England]; New York, 1999.

2. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.

3. Schaubert, D., D. Wilton, and A. Glisson, "A tetrahedral modeling method for electromagnetic scattering by arbitrarily shaped inhomogeneous dielectric bodies," IEEE Trans. Antennas Propagat., Vol. 32, No. 1, 77-85, 1984.
doi:10.1109/TAP.1984.1143193

4. Richmond, J., "Scattering by a dielectric cylinder of arbitrary cross section shape," IEEE Trans. Antennas Propagat., Vol. 13, No. 3, 334-341, 1965.
doi:10.1109/TAP.1965.1138427

5. —, "TE-wave scattering by a dielectric cylinder of arbitrary cross-section shape," IEEE Trans. Antennas Propagat., Vol. 14, No. 4, 460-464, 1966.
doi:10.1109/TAP.1966.1138730

6. Rubin, B. J., "Divergence-free basis for representing polarization current in finite-size dielectric regions," IEEE Trans. Antennas Propagat., Vol. 41, No. 3, 269-277, 1993.
doi:10.1109/8.233137

7. Wu, W. L., A. Glisson, and D. Kajfez, "A study of two numerical solution procedures for the electric field integral equation at low frequency," ACES J., Vol. 10, No. 3, 69-80, 1995.

8. Vecchi, G., "Loop-star decomposition of basis functions in the discretization of the EFIE," IEEE Trans. Antennas Propagat., Vol. 47, No. 2, 339-346, 1999.
doi:10.1109/8.761074

9. Zhao, J. S. and W. C. Chew, "Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies," IEEE Trans. Antennas Propagat., Vol. 48, No. 10, 1635-1645, 2000.
doi:10.1109/8.899680

10. Lee, J. F., R. Lee, and R. J. Burkholder, "Loop star basis functions and a robust pre-conditioner for EFIE scattering problems," IEEE Trans. Antennas Propagat., Vol. 51, No. 8, 1855-1863, 2003.
doi:10.1109/TAP.2003.814736

11. Eibert, T. F., "Iterative-solver convergence for loop-star and loop-tree decompositions in method-of-moments solutions of the electric-field integral equation," IEEE Antennas Propagat. Mag., Vol. 46, No. 3, 80-85, 2004.
doi:10.1109/MAP.2004.1374101

12. Mendes, L. S. and S. A. Carvalho, "Scattering of EM waves by homogeneous dielectrics with the use of the method of moments and 3D solenoidal basis functions," Micro. Opt. Tech. Lett., Vol. 12, No. 6, 327-331, 1996.
doi:10.1002/(SICI)1098-2760(19960820)12:6<327::AID-MOP7>3.0.CO;2-H

13. Carvalho, S. A. and L. S. Mendes, "Scattering of EM waves by inhomogeneous dielectrics with the use of the method of moments and the 3D solenoidal basis functions," Micro. Opt. Tech. Lett., Vol. 23, No. 1, 42-46, 1999.
doi:10.1002/(SICI)1098-2760(19991005)23:1<42::AID-MOP12>3.0.CO;2-N

14. Kulkarni, S., R. Lemdiasov, R. Ludwig, and S. Makarov, "Comparison of two sets of low-order basis functions for tetrahedral VIE modeling," IEEE Trans. Antennas Propagat., Vol. 52, No. 10, 2789-2794, 2004.
doi:10.1109/TAP.2004.834377

15. Gan, H. and W. C. Chew, "A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems," J. Electromagn. Waves Appl., Vol. 9, No. 10, 1339-1357, 1995.

16. Rao, G. R. W. S. M and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, No. 3, 409-418, 1982.
doi:10.1109/TAP.1982.1142818

17. Chao, H.-Y. R., "A multilevel fast multipole algorithm for analyzing radiation and scattering from wire antennas in a complex environment," Ph.D. dissertation, 2002.

18. Shaffer, C. A., A Practical Introduction to Data Structures and Algorithm Analysis, 2nd ed., Prentice Hall, Upper Saddle River, NJ, 2001.

19. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Boston, 2001.

20. Bai, L., "An efficient algorithm for finding the minimal loop basis of a graph and its application in computational electromagnetics," M.S. thesis, 2000.

21. Keener, J. P., Principles of Applied Mathematics: Transformation and approximation, rev. ed., Perseus Books, Advanced Book Program, Cambridge, MA, 2000.

22. Golub, G. H., Matrix Computations, Johns Hopkins University Press, Baltimore, 1996.


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