| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 94 === In this thesis, a numerical algorithm for solving the ElectroMagnetic (EM) waveguide, EM resonator and electromagnetic wave scattering problems, involving 2-D and 3-D Helmholtz equation, is described and implemented. In the Method of Fundamental Solutions (MFS), seeding location of the source points on a fictitious boundary off-setting from the real boundary is necessary. However, in the proposed method the double-layer potential kernel functions are employed as the alternative radial basis functions (RBFs) in the conventional MFS which uses the fundamental solutions, seeding the source points on the real boundary, and the source points coincide with the boundary points, causing hypersingularity occurs. The purpose of above-mentioned statements is to derive the diagonal terms of the influence matrices by using a desingularization technique to regularize the singularity and hypersingularity of the Green’s functions. Applying the proposed method in which the meshless features of the MFS are maintained yields a reliable solution. Numerical simulations consist of the solutions of electromagnetic waveguide, resonator and 3-D electromagnetic wave scattering problems. Numerical examples are performed, and compared the present numerical results with the analytical solutions, results of conventional MFS and other numerical methods. The validity and accuracy of the proposed method are well demonstrated.
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