A fast elastostatic solver based on fast Fourier transform on multipoles (FFTM)

Abstract

In this paper, we present a fast algorithm to solve elasticity problems, governed by the Navier equation, using the boundary element method (BEM). This fast algorithm is based on the fast Fourier transform on multipoles (FFTM) method that has been developed for the Laplace equation. The FFTM method uses multipole moments and their kernel functions, together with the fast Fourier transform (FFT), to accelerate the far field computation. The memory requirement of the original FFTM tends to be high, especially when the method is extended to the Navier equation that involves vector quantities. In this paper, we used a compact representation of the translation matrices for the Navier equation based on solid harmonics. This reduces the memory usage significantly, allowing large elasticity problems to be solved efficiently. The improved FFTM is compared with the commonly used FMM, revealing that the FFTM requires shorter computational time but more memory than the FMM to achieve comparable accuracy. Finally, the method is applied to calculate the effective Young's modulus of a material containing numerous voids of various shapes, sizes and orientations. Copyright © 2008 John Wiley & Sons, Ltd.