The Fast Fourier transform on multipoles (FFTM) method for three-dimensional electrostatics field analysis

The Fast Fourier transform on multipoles (FFTM) method is developed for efficient solution of the boundary element method. The method employs the multipole/local expansions to approximate the far field potentials, and uses the fast Fourier transform (FFT) to accelerate the translations of the multipole to local expansions due to its convolution nature. This paper reports the results of using the FFTM algorithm for solving large-scale three-dimensional electrostatics field problems. It is demonstrated that the method can give accurate results both in terms of the calculated capacitance and the surface charge density distributions. It is also found that FFTM has computational complexities of O(N-a), where a ranges from 1.0 to 1.4 for the computational time, and from 1.1 to 1.2 for the memory storage requirements.