Vol. 52
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2004-12-13
Error Estimation of the Method of Auxiliary Sources (Mas) for Scattering from an Impedance Circular Cylinder
By
, Vol. 52, 109-128, 2005
Abstract
The purpose of this paper is a rigorous error estimation of the Method of Auxiliary Sources (MAS), when the latter is applied to electromagnetic scattering from a circular, coated, perfectly conducting cylinder, assumed to satisfy the Standard Impedance Boundary Condition (SIBC). The MAS matrix is inverted analytically, via eigenvalue analysis, and an exact expression for the discretization error in the boundary condition is derived. Furthermore, an analytical formula for the condition number of the linear system is also extracted, in addition to an asymptotic estimate for large scatterers, explaining the irregular behavior of the computational error resulting from numerical matrix inversion. Finally, the optimal location of the auxiliary sources is determined, on the grounds of error minimization.
Citation
Hristos Anastassiu , "Error Estimation of the Method of Auxiliary Sources (Mas) for Scattering from an Impedance Circular Cylinder," , Vol. 52, 109-128, 2005.
doi:10.2528/PIER04072101
http://www.jpier.org/PIER/pier.php?paper=0407211
References

1. Popovidi, R. S. and Z. S. Tsverikmazashvili, "Numerical study of a diffraction problem by a modified method of non-orthogonal series," Journal of Applied Mathematics and Mathematical Physics, Vol. 17, No. 2, 384-393, 1977.

2. Doicu, A., Yu. Eremin, and T. Wriedt, Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources, Academic Press, New York, 2000.

3. Fairweather, G., A. Karageorghis, and P. A. Martin, "The method of fundamental solutions for scattering and radiation problems," Engineering Analysis with Boundary Elements, Vol. 27, 759-769, 2003.
doi:10.1016/S0955-7997(03)00017-1

4. Golberg, M. A. and C. S. Chen, "The method of fundamental solutions for potential, Helmholtz and diffusion problems," Boundary Integral Methods and Mathematical Aspects, 103-176, 1999.

5. Leviatan, Y., Am. Boag, and Al. Boag, "Analysis of electromagnetic scattering from dielectrically coated conducting cylinders using a multifilament current model," IEEE Transactions on Antennas and Propagation, Vol. AP-36, No. 11, 1602-1607, 1988.
doi:10.1109/8.9711

6. Leviatan, Y., "Analytic continuation considerations when using generalized formulations for scattering problems," IEEE Trans. on Antennas and Propagation, Vol. AP-38, No. 8, 1259-1263, 1990.
doi:10.1109/8.56964

7. Kaklamani, D. I. and H. T. Anastassiu, "Aspects of the method of auxiliary sources (MAS) in computational electromagnetics," IEEE Antennas and Propagation Magazine, Vol. 44, No. 3, 48-64, 2002.
doi:10.1109/MAP.2002.1028734

8. Anastassiu, H. T., D. I. Kaklamani, D. P. Economou, and O. Breinbjerg, "Electromagnetic scattering analysis of coated conductors with edges using the method of auxiliary sources (MAS) in conjunction with the standard impedance boundary condition (SIBC)," IEEE Trans. on Antennas and Propagation, Vol. AP-50, No. 1, 59-66, 2002.
doi:10.1109/8.992562

9. Anastassiu, H. T., D. G. Lymperopoulos, and D. I. Kaklamani, "Accuracy analysis and optimization of the method of auxiliary sources (MAS) for scattering by a circular cylinder," IEEE Trans. on Antennas and Propagation, Vol. AP-52, No. 6, 1541-1547, 2004.
doi:10.1109/TAP.2004.830264

10. Anastassiu, H. T. and D. I. Kaklamani, "Error estimation and optimization of the method of auxiliary sources (MAS) applied to TE scattering by a perfectly conducting circular cylinder," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 10, 1283-1294, 2004.
doi:10.1163/1569393042954947

11. Warnick, K. F. and W. C. Chew, "Accuracy of the method of moments for scattering by a cylinder," IEEE Trans. Microwave Theory and Techniques, Vol. MTT-48, No. 10, 1652-1660, 2000.
doi:10.1109/22.873892

12. Hochstadt, H., The Functions of Mathematical Physics, Dover, New York, 1986.

13. Senior, T. B. A. and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, IEE Press, 1994.

14. Abramowitz, A. and I. E. Stegun, Handbook of Mathematical Functions, Dover, New York, 1972.

15. Kouyoumjian, R., EE805 course notes, The Ohio State University, Columbus OH, 1990.

16. Davies, P. J., Circulant Matrices, Wiley, New York, 1979.

17. Smyrlis, Y. and A. Karageorghis, "Numerical analysis of the MFS for certain harmonic problems," Modelisation Mathematique et Analyse Numerique, Vol. 38, 495-517, 2004.
doi:10.1051/m2an:2004023