Performance Evaluation of 2nd Order Localized Approximation in Predicting Internal Electric Field in One-Dimensional Slab Problem
AbstractWe investigate the performance of a new 2nd order localized ap-proximation, as extracted from the generalization of the localized ap-proximation. These 2nd order localized approximation is then appliedin the study of electromagnetic field interaction of plane waves with aslab of complex conductivity. The approximation allowed us to obtainexplicit expressions for the internal electric field of the one dimen-sional slab from the integral equations for a piece-wise constant andlinear profiles. These equations were employed to compute the inter-nal electric fields within the slab support. The computed results werecompared with the exact solutions obtained from transmission-linetheory. In addition we iteratively solved for the internal electric fieldfrom the intergral equations. The three solutions were then evaluatedand compared at two distinct frequencies. The effect of backgroundprofile and contract between the slab and background profiles on theaccuracy of the approximation were thoroughly investigated in detail.We also derived explicit expressions for the internal electric field fora slab with linear complex conductivity profile. However, these werenever numerically computed and evaluated. We defined as L2 er-ror norm, with reference to the exact solution from Transmission-linetheory as a metric for the performance evaluation of the computedinternal fields. The results are presented in both graphical and table1forms. The Original Habashy approximation solutions were comparedagainst the new 2nd order solutions. We conclude with evaluation ofthe performances of the approximations and recommendations for thenext logical direction in future investigation of the localized approxi-mations.
How to Cite
Adopley, J. (2014). Performance Evaluation of 2nd Order Localized Approximation in Predicting Internal Electric Field in One-Dimensional Slab Problem. Asian Journal of Engineering and Technology, 2(1). Retrieved from https://ajouronline.com/index.php/AJET/article/view/839
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