Modeling of patch antennas and resonators on arbitrary dielectric substrates using surface RWG and volume edge based basis functions and the Method of Moments is implemented. The performance of the solver is studied for different mesh configurations. The results obtained are tested by comparison with experiments and Ansoft HFSS v9 simulator. The latter uses a large number of finite elements (up to 200K) and adaptive mesh refinement, thus providing the reliable data for comparison. The error in the resonant frequency is estimated for canonical resonator structures at different values of the relative dielectric constant ƒÕr, which ranges from 1 to 200. The reported results show a near perfect agreement in the estimation of resonant frequency for all the metal-dielectric resonators. Behavior of the antenna input impedance is tested, close to the first resonant frequency for the patch antenna. The error in the resonant frequency is estimated for different structures at different values of the relative dielectric constant ƒÕr, which ranges from 1 to 10. A larger error is observed in the calculation of the resonant frequency of the patch antenna. Moreover, this error increases with increase in the dielectric constant of the substrate. Further scope for improvement lies in the investigation of this effect.

Computational electromagnetic modeling involves generating system matrices by discretizing integral equations and solving the resulting system of linear equations. Many methods of solving the system of linear equations exist and one such method is the factorization of the matrix using the so called local-global solution (LOGOS) modes. Computer codes to perform the discretization of the integral equations, filling of the matrix, and the subsequent LOGOS factorization have previously been developed by others. However, these codes are limited to complex double precision arithmetic only. This thesis extends and expands the existing computer by creating a more general implementation that is able to analyze a problem not only in complex double precision but also in real double precision and both complex and real single precision. The existing code is expanded using "templates" in Fortran 90 and the resulting generic code is used test the performance of the LOGOS (both OL- and NL-LOGOS) factorization on matrices generated by discretization of the volume integral equation. As part of this effort, we demonstrate for the first time that the LOGOS factorization provides an O(N log N) complexity solution to the volume integral equation formulation of low-frequency electromagnetic problems.

<p>Among computational electromagnetic methods, Integral Equation (IE) solvers have a great capability in solving open-region problems such as scattering and radiation, due to no truncation boundary condition required. Volume Integral Equation (VIE) solvers are especially capable of handling arbitrarily shaped geometries and inhomogeneous materials. However, the numerical system resulting from a VIE analysis is a dense system, having $N^2$ nonzero elements for a problem of $ N $ unknowns. The dense numerical system in conjunction with the large number of unknowns resulting from a volume discretization prevents a practical use of the VIE for solving large-scale problems.</p> <p>In this work, two fast algorithms of $ O(N \log N) $ complexity to generate an rank-minimized $ H^2 $-representation for electrically large VIEs are developed. The algorithms systematically compress the off-diagonal admissible blocks of full VIE matrix into low-rank forms of total storage of $O(N)$. Both algorithms are based on nested cross approximation, which are purely algebraic. The first one is a two-stage algorithm. The second one is optimized to only use one-stage, and has a significant speedup. Numerical experiments on electrically large examples with over 33 million unknowns demonstrate the efficiency and accuracy of the proposed algorithms. </p> <p>Important applications of VIEs in thermal and quantum engineering have also been explored in this work. Creating spin(circularly)-polarized infrared thermal radiation source without an external magnetic field is important in science and engineering. Here we study two materials, magnetic Weyl semimetals and manganese-bismuth(MnBi), which both have permittivity tensors of large gyrotropy, and can emit circularly-polarized thermal radiations without an external magnetic field. We also design symmetry-broken metasurfaces, which show strong circularly-polarized radiations in simulations and experiments. In spin qubit quantum computing systems, metallic gates and antennas are necessary for quantum gate operations. But their existence greatly enhances evanescent wave Johnson noise (EWJN), which induces the decay of spin qubits and limits the quantum gate operation fidelity. Here we first use VIE to accurately simulate realistic quantum gate designs and quantify the influence on gate fidelity due to this noise.</p>