Parallelized Solution Method of the Three-dimensional Gravitational Potential on the Yin-Yang Grid

TL;DR

This paper introduces a parallelized, efficient method for computing the 3D gravitational potential on the Yin-Yang grid, leveraging multipole decomposition and optimized communication for distributed-memory systems.

Contribution

It presents a novel symmetric algorithm that minimizes data communication and operates directly on the grid without auxiliary interpolation, improving computational efficiency.

Findings

Efficient parallel computation on distributed-memory systems.

Reduced data communication due to symmetric multipole decomposition.

Operates directly on the original grid without auxiliary interpolation.

Abstract

We present a new method for solving the three-dimensional gravitational potential of a density field on the Yin-Yang grid. Our algorithm is based on a multipole decomposition and completely symmetric with respect to the two Yin-Yang grid patches. It is particularly efficient on distributed-memory machines with a large number of compute tasks, because the amount of data being explicitly communicated is minimized. All operations are performed on the original grid without the need for interpolating data onto an auxiliary spherical mesh.