| Summary: | 碩士 === 國立臺灣大學 === 土木工程學研究所 === 89 === In this study , the non-singular boundary integral equation method was used to circumvent the numerical singularity in traditional Boundary Element Method (BEM) . First of all , the non-singular boundary integral equations for the Laplace (Poisson) equation , the Helmholtz equation and the modified Helmholtz equation were derived by Gauss flux theorem and equal-potential theory . Then , the 2D Stokes flow of a circular cavity and a square cavity was computed by the velocity-vorticity formulation , the Biot-Savart law and the non-singular boundary integral equation for the Laplace equation . The velocity-vorticity formulation and the non-singular boundary integral equation for the modified Helmholtz equation are adopted to calculate the low Reynolds number flow field in a square cavity . In a square waveguide , the distributions of electromagnetic propagation for TE and TM modes were found by the non-singular boundary integral equation for the Helmholtz equation . All of the numerical simulations are compared with analytic solutions and other numerical results . The study shows that the non-singular boundary integral equations can get the most efficient and accurate results in solving some engineering problems associated with the governing equations of the Laplace , Poisson , Helmholtz , and modified Helmholtz equations .
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