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2006-05-20
Sparse Factorization of the Tmz Impedance Matrix in an Overlapped Localizing Basis
By
Progress In Electromagnetics Research, Vol. 61, 291-322, 2006
Abstract
It has been observed that localized solution modes provide sparse factored representations of the discrete integral equations encountered in the simulation of electromagnetic phenomena at low frequencies. This paper extends these results by incorporating overlapped localizing modes. For TMz scattering from a rectangular array of perfectly conducting obstacles, it is observed that the complexity scaling of the resulting factorization is significantly reduced relative to previously reported results. The memory complexity of the resulting factored representation scales approximately as O(N) for electrically small arrays. Limitations and possible extensions of these results are discussed.
Citation
Robert Adams A. Zhu Francis Canning , "Sparse Factorization of the Tmz Impedance Matrix in an Overlapped Localizing Basis," Progress In Electromagnetics Research, Vol. 61, 291-322, 2006.
doi:10.2528/PIER06022402
http://www.jpier.org/PIER/pier.php?paper=0602242
References

1. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, IEEE Press, New York, 1998.

2. Adams, R. J., G. Wang, and F. X. Canning, "Efficient inversion of the impedance matrix in an overlapping, localizing basis," USNC- URSI National Radio Science Meeting, No. 1, 2006.

3. Adams, R. J., F. X. Canning, and A. Zhu, "Sparse representations of integral equations in a localizing basis," Microwave and Optical Technology Letters, Vol. 47, 236-240, 2005.
doi:10.1002/mop.21135

4. Adams, R. J., F. X. Canning, and A. Zhu, "Fast solution of integral equations in a localizing basis," IEEE AP-S International Symposium and USNC/URSI National Radio Science Meeting, No. 7, 2005.

5. Adams, R. J., A. Zhu, and F. X. Canning, "Efficient solution of integral equations in a localizing basis," Journal of Electromagnetic Waves and Applications, Vol. 19, 1583-1594, 2005.
doi:10.1163/156939305775537438

6. Zhu, A., R. J. Adams, F. X. Canning, and S. D. Gedney, "Sparse solution of an integral equation formulation of scattering from open PEC targets," Microwave and Optical Technology Letters, Vol. 48, 476-480, 2006.
doi:10.1002/mop.21383

7. Zhu, A., R. J. Adams, F. X. Canning, and S. D. Gedney, "Schur factorization of the impedance matrix in a localizing basis," Journal of Electromagnetic Waves and Applications, Vol. 20, 351-362, 2006.
doi:10.1163/156939306775701803

8. Bebendorf, M., "Approximation of boundary element matrices," Numerische Mathematik, Vol. 86, 565-589, 2000.
doi:10.1007/PL00005410

9. Zhu, A., R. J. Adams, and F. X. Canning, "Multilevel simply sparse method for scattering by PEC," IEEE AP-S International Symposium and USNC/URSI National Radio Science Meeting, Vol. 4A, No. 7, 427-430, 2005.

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

11. Canning, F. X. and K. Rogovin, "A universal matrix solver for integral-equation-based problems," IEEE Antennas and Propagation Magazine, Vol. 45, 19-26, 2003.
doi:10.1109/MAP.2003.1189648

12. Bucci, O., "On the degrees of freedom of scattered fields," IEEE Transactions on Antennas and Propagation, Vol. 37, 1989.