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Browsing by Author "Albayaty, Abdullah Omran Ali"

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    Master Thesis
    Improvements in the finite element method and method of moments for the solution of electromagnetic problems
    (Çankaya Üniversitesi, 2017) Albayaty, Abdullah Omran Ali
    In this thesis, two numerical techniques, the finite element method (FEM) and the method of moments (MoM) are improved for solving electromagnetic boundary value problems governed by differential and integral equations. The FEM is a numerical technique used to solve differential equations. The solution domain is divided into small intervals (elements), and the unknown function is calculated by finding an approximate solution by a truncated series of different shape functions. This approximate solution can be replaced with the original function in the differential equation. As a result, we get the matrix of equations that can be solved to obtain separate solution to the problem. In this thesis, we used the sigmoid function as a novel application, and compare the accuracy of FEM with the sigmoid function against the well-known linear and the step functions. Two examples of electromagnetic problems are presented. It is concluded that the sigmoid function under specific conditions yields the most accurate results. For MoM, this thesis presents a new mathematical algorithm for the solution of electromagnetic problems. This algorithm is schemed to be suitable for solving the singularity that exists in the solution matrix. This adaptive integration algorithm aims to avoid the singularity in the evaluation of the integral so called the Cauchy Principal Value integral. An example electrostatic problem is presented and it is proved that the novel method is accurate.