Accurate and efficient three-dimensional electrostatics analysis using singular boundary elements and Fast Fourier Transform on Multipole (FFTM)

Abstract

This thesis describes two methods of improving the accuracy and efficiency of three-dimensional electrostatics analysis. The accuracy is improved by developing new singular boundary elements to deal with corner and edge singularity problems. These singular elements can accurately represent the singularity behaviour of the edges and corners, because they include the correct order of singularity in the formulations of the shape functions. A fast algorithm called the Fast Fourier Transform on Multipoles (FFTM) is also proposed for the efficient solution of the integral equation in the boundary element method. Based on the numerical simulations, the method is observed to exhibit approximately linear growth in terms of computational time and storage requirements. The speedup in the algorithm is achieved by: (i) using the multipole expansion to approximate a??distanta?? potential fields, and (ii) evaluating the approximate potential fields rapidly by discrete convolution via FFT.