The Use of parabolic interpolation functions in analyzing electrostatic field problems by the boundary element method

ABSTRACT Master Thesis THE USE OF PARABOLIC INTERPOLATION FUNCTIONS IN ANALYZING ELECTROSTATIC FIELD PROBLEMS BY THE BOUNDARY ELEMENT METHOD Belkıs ERİŞTİ Fırat University Graduate School of Natural and Applied Sciences Department of Electrical Education 2003, Page: 78 In this study, two dimensional electrostatic field problems have been calculated by using the parabolic boundary elements of the Boundary Element Method. Furthermore, constant and linear boundary elements were investigated and the three different programs belong to three boundary elements were developed. For this purpose, the region equations, which were described by the Laplace and Poisson equations, were obtained into boundary integral equations by the help of Green's formula and the method of weighted residuals. Boundary integral equations were discretized with parabolic boundary elements written in the matrix form. In this matrix form, influence coefficients are calculated by the method of numerical Gauss integration and single integrals were calculated analytically. Unknown boundary variables were calculated by solving the equation system, which is composed of boundary unknowns, by applying Dirichlet and Neumann boundary conditions. Then calculated and defined values were used to find the voltage values at the internal points of the region. As the result, three developed programs were applied to planar samples of electrodes and coaxial cables and the values obtained are compared with the analytical calculations. Key Words: Boundary Element Method, Boundary Integral Equation, Electrostatic Field, Equations of Laplace and Poisson, Constant Element, Linear Element, Parabolic Element. VIII