| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 90 === In order to avoid dealing with the numerical singularity directly, the non-singular boundary integral equation for Helmholtz equation is presented in this study. By employing Gauss flux theorem and the concept of equipotential, the singularity would be eliminated from the integral and therefore no special treatment is necessary for the computation of singular integral. After the non-singular boundary integral equation is deduced, it will be applied to some electromagnetic wave propagation problems. First, this numerical model is chosen to calculate and analyze the distributions of electric and magnetic fields for and mode in rectangular 2D waveguide and 3D cavity resonator. Because the governing equations are transformed from Maxwell’s equations into Helmholtz equations in frequency domain, and all the known boundary values are equal to zero due to the simplified assumptions of numerical simulation. In this study we utilize the singular value decomposition (SVD) technique to find out the eigenvalues, their multiplicities and the non-trivial solutions. Furthermore, this study also dealed with the applications of non-singular boundary integral equation to the electromagnetic scattering of plane waves by a perfect electric conducting cylinder in 2D and sphere in 3D, respectively. All the numerical results are compared with analytical solutions to verify this numerical model. It is concluded that the non-singular boundary integral equation is much simpler and more efficient, as far as simulations of 2D and 3D Helmholtz equations are concerned.
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