Regularized spectral multipole BEM for plane elasticity
A multipole algorithm for plane elasticity based on the direct boundary element method (BEM) is presented. The kernels in the BEM are approximated as truncated Taylor series with expansion points taken from a uniform grid. The algorithm replaces the usual BEM elemental summations with correlation sums on the regular grid in terms of the sampled kernel data and density moments. Far field influences are rapidly computed in the frequency domain using the fast Fourier transform (FFT). The resultant linear system of equations is solved with GMRES. The multipole method is extended to whole-body regularized forms of the standard displacement-BIE and the stress-BIE. Free-term coefficients which arise from regularization in the far field are also rapidly computed as correlation sums with the FFT. The algorithm is shown to be faster than the traditional BEM for models with over 400 quartic elements while maintaining an acceptably high level of accuracy.
regularization multipole elasticity boundary element method fast fourier transform hypersingular