The Error Cross-Section Method for Quantifying the Error in Electromagnetic Scattering Problems
关键词:
CFIE, numerical error, radar crosssection摘要
The Error Cross-Section (ECS) is introduced to quantify the error associated with the numerical solution of electromagnetic scattering problems. The ECS accounts for different approximations and inaccuracies in the object discretization and numerical computations. The ECS definition is based on the power conservation principle and is visualized by comparing it to the radar cross-section of a thin wire for twodimensional (2-D) problems or a small sphere for three-dimensional (3-D) problems. The proposed ECS method is independent of the adopted numerical technique and therefore can be used to give confidence in the obtained solution using several methods, such as the Method of Moments (MoM) and the Finite-Difference FrequencyDomain (FDFD) method. Application of the ECS to the optimization of certain parameters for some numerical formulations, such as the CombinedField Integral Equation (CFIE) is also presented.
##plugins.generic.usageStats.downloads##
参考
J. Liu and J. M. Jin, “A special higher order finiteelement method for scattering by deep cavities,” IEEE Transactions on Antennas and Propagation, vol. 48, no. 5, pp. 694-703, 2000.
R. Luebbers, D. Steich and K. Kunz, “FDTD calculation of scattering from frequency-dependent materials,” IEEE Transactions on Antennas and Propagation, vol. 41, no. 9, pp. 1249-1257, 1993.
E. Lucente, A. Monorchio and R. Mittra, “An iteration-free MoM approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems,” IEEE Transactions on Antennas and Propagation, vol. 56, no. 4, pp. 999-1007, 2008.
J. M. Jin and V. V. Liepa, “Application of hybrid finite element method to electromagnetic scattering from coated cylinders,” IEEE Transactions on Antennas and Propagation, vol. 36, no. 1, pp. 50- 54, 1988.
C. P. Davis and K. F. Warnick, “Error analysis of 2-D MoM for MFIE/EFIE/CFIE based on the circular cylinder,” IEEE Transactions on Antennas and Propagation, vol. 53, no. 1, pp. 321-331, 2005.
G. C. Hsiao and R. E. Kleinman, “Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 3, pp. 316-328, 1997.
F. Wei, J. W. Massey, C. S. Geyik and A. E. Yilmaz, “Error measures for comparing bioelectromagnetic simulators,” Antennas and Propagation Society International Symposium (APSURSI), IEEE, pp. 1-2, 2012.
K. F. Warnick and W. C. Chew, “Error analysis of the moment method,” Antennas and Propagation Magazine, IEEE, vol. 46, no. 6, pp. 38-53, 2004.
C. P. DAVIS and K. F. Warnick, “The physical meaning of the Sobolev norm in error estimation,” National Radio Science Meeting, pp. 3377-3380, 2004.
C. A. Balanis and J. Wiley, “Advanced engineering electromagnetics,” Wiley Online Library, vol. 111, 2012.
W. C. Chew, E. Michielssen, J. Song and J. Jin, “Fast and efficient algorithms in computational electromagnetics,” Artech House, Inc., 2001.
J. R. Mautz and R. F. Harrington, “H-field, e-field, and combined-field solutions for conducting bodies of revolution,” Archiv Elektronik und Uebertragungstechnik, vol. 32, pp. 157-164, 1978.
