Convergence and error study of different basis and testing functions in the method of moments applied to electromagnetic wave scattering from dielectric objects

The convergence and variation of error of numerical methods depends on the implementation of different types of basis and testing functions. This thesis describes a comparative analysis of different basis and testing functions used in the MoM for two dimensional dielectric objects. The basis and testing functions namely the sinusoid/pulse (SP), sinusoid/sinusoid (SS), sinusoid/triangle (ST), triangle/pulse (TP), triangle/sinusoid (TS) and triangle/triangle (TT) methods are considered in this work. These basis and testing functions used in conjunction with MoM integral equations which include the electric field integral equation (EFIE), magnetic field integral equation (MFIE), Poggio-Muller-Chu-Harrington-Wu (PMCHW) integral equation and the Muller integral equation. All the computations in this study are carried out using MATLAB on dielectric objects using personal computer with 2GB DDR3 RAM. The variation of mean relative error with samples per wavelength is calculated for different dielectric objects with outer and inner radii of 0.0521 m and 0.0313 m respectively. Using Gauss quadrature technique, the SP and TP methods give faster convergence than the SS, ST, TS and TT methods for a higher number of integral equations at 915 MHz. When the EFIE and MFIE are used in both TE and TM cases of the hollow dielectric cylinder with relative permittivity of 77.3-j37.2, the SS,ST,TS and TT methods require at least 1.5 and 1.75 times the samples per wavelength required by the SP and TP methods to achieve magnetic current error less than 0.01 respectively. For the dielectric coated conducting cylinder with relative permittivity of 33.2-j124.17, the SS, ST, TS and TT methods require 2 times the samples per wavelength required by the SP and TP methods for the surface magnetic current calculated using Gauss quadrature technique to be more accurate than the staircase approximation technique. The difference in the convergence due to different basis and testing function under the impedance boundary condition (IBC) is not as significant as under the exact boundary condition (EBC) for the dielectric coated impedance cylinder. The difference in the number of matrix elements between the SS, ST and SP methods and also between the TS, TT and TP methods to achieve magnetic current error less than 0.01 for the Muller integral equation is higher than the EFIE and MFIE when the EBC is utilised. The SP and TP methods provide faster convergence than the SS, ST, TS and TT methods with a higher difference in the number of matrix elements between the SS, ST and SP methods and also between the TS, TT and TP methods to achieve an error less than 0.01 for the high permittivity hollow dielectric cylinder with large size compared to the one with small size.

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