A kernel-independent uniform fast multipole method based on barycentric rational interpolation

A kernel-independent uniform fast multipole method (UFMM) is presented for fast summation of particle interactions, where the kernel is approximated by using the Floater-Hormann (FH) rational interpolant at the equispaced grids. The proposed UFMM is stable and allows for reducing the cost of the moment-to-local translation (M2L) operators dramatically accelerated by fast Fourier transform (FFT). Moreover, the accuracy can be improved as the number of nodes increases. In addition, a modified smooth-UFMM for some sufficiently smooth kernels is considered, which has better performance than the originally smooth-UFMM. The efficiency and accuracy are illustrated by numerical examples arising from the method of the regularized Stokeslets (MRS) and inverse quadratic kernels.