A new method for computing self-gravity in an isolated system

TL;DR

This paper introduces a new approximation method for solving Poisson's equation in isolated systems, reducing errors near boundaries and allowing systematic error control, demonstrated through 2D and 3D numerical examples.

Contribution

The paper presents a novel image multipole method for computing self-gravity that minimizes errors in the source region and offers systematic error reduction capabilities.

Findings

Error near boundary is minimized compared to existing methods

Method effectively reduces errors with increased computational effort

Numerical examples demonstrate improved accuracy in 2D and 3D cases

Abstract

A new approximation method for inverting the Poisson's equation is presented for a continuously distributed and finite-sized source in an unbound domain. The advantage of this image multipole method arises from its ability to place the computational error close to the computational domain boundary, making the source region almost error free. It is contrasted to the modified Green's function method that has small but finite errors in the source region. Moreover, this approximation method also has a systematic way to greatly reduce the errors at the expense of somewhat greater computational efforts. Numerical examples of three-dimensional and two-dimensional cases are given to illustrate the advantage of the new method.