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Title: The Method of Auxiliary Sources in electromagnetic problems of scattering, mode analysis, and shielding: Theory and Applications
Authors: Kouroumplakis, Minas
Φικιώρης Γεώργιος
Keywords: Method of Auxiliary Sources, Convergence and Divergence, mode analysis, response function, Auxiliary Current Vector Norm, Hybrid Modes, Graphene, Electromagnetic Shielding, Electromagnetic Scattering.
Issue Date: 13-Jul-2022
Abstract: The most common choice for the numerical solution of integral equations is the Method of Moments (MoM). However, during its implementation, and in particular, when filling the impedance matrix, it is necessary to calculate singular integrals due to the integration on the boundary surface or curve. This sometimes results in an approximate solution of the EM fields in a specified domain, which might be unacceptable. For the above and other reasons, a group of methods known as Generalized Multipole Techniques (GMT’s) have been developed over many years. One of the methods of GMT’s is the Method of Auxiliary Sources (MAS). In general MAS is a very effective method for solving boundary value problems with the main advantages being the simplicity of implementation, low memory usage, and fast computation of the results. On the other hand, the application of MAS might be problematic in cases where we have divergence of current amplitudes, or might need modification in order to deal with the appearance of spurious solutions in mode analysis, and when field calculation is required in areas with high conductivity, such as shielding materials. The dissertation deals with the application of MAS in geometries in which problems of this nature arise. Specifically, we apply MAS to EM scattering problems from Perfect Electric Conductor (PEC) cylinders, with the main purpose of studying the effect of divergence of auxiliary current amplitudes on the numerical results for the EM fields. The MAS is then applied to calculate the eigenvalues of simply and multiply connected PEC waveguides with an arbitrary cross section. To address the problem of spurious eigenvalues, a modified version of standard MAS is applied in which the waveguide is driven by an excitation source such as a point source or a plane wave. This modified method is termed as MAS with an Excitation Source (MAS-ES). The eigenvalues are calculated by detecting the wavenumbers for which the waveguide cross section resonates with the excitation source. Resonance is detected by the values of a properly defined response-function. Then we extend the MAS-ES by proving that the resonances of the waveguide are also detected by observing the peak values of the Auxiliary Current Vector Norm (ACVN). The advantages of this approach over the response-function approach are the simplicity of the algorithm, the clarity of the response curve, and the computation time. In addition, an algorithm is presented with which a very fast calculation of the impedance matrix is achieved. Additionally we show that MAS-ES applies in the case of dielectric waveguides. Since dielectric waveguides support hybrid modes, two excitation sources are required simultaneously, an electric and magnetic, in order to obtain correct eigenvalues. This results to what we call MAS with Two Excitation Sources (MAS-TES). It is numerically demonstrated that if the excitation sources are placed inside an optimum curve within the core, no spurious solutions appear in the response curve. Lastly, the evaluation of monolayer graphene (MLG) as a material suitable for EM shielding in the RF/microwave region is investigated. The high conductivity of graphene at RF frequencies in combination with other properties such as transparency in the optical spectrum, mechanical strength, elasticity, thermal conductivity, etc. make it an ideal material for EM shielding. Numerical experiments on cylindrical configurations shielded by graphene which is deposited on silicon dioxide are performed. Since standard MAS encounters difficulties when computing the fields in highly conductive regions, a modified MAS is proposed according to which graphene is replaced by an Impedance Matrix Boundary Condition (MAS with IMBC). This way, we avoid calculating the fields inside graphene.
Appears in Collections:Διδακτορικές Διατριβές - Ph.D. Theses

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