A Numerical Convolution Representation of Potential for a Disk Surface Density in 3D

Abstract

This study presents a numerical convolution representation of a potential induced from a disk of surface density, which has often been investigated in the center region of galaxies. The advantage of this representation is to release the softening length for the $N$-body method and artificial boundary conditions for the spectral methods. With the help of fast Fourier transform, the computational complexity is only $O(M^2({\log }_{2}M))$, where $M$ is the number of zones in one dimension. Numerical results show an almost second order of accuracy on a Cartesian coordinate system. A comparison study also demonstrates that this method can calculate the potential for disk surface density based on the uniform grids.