Work

A Fast, Second-order Accurate Poisson Solver in Spherical Polar Coordinates

Year: 2025

Type: article

Abstract: We present an efficient and accurate algorithm for solving the Poisson equation in spherical polar coordinates with a logarithmic radial grid and open boundary conditions. The method employs a divide-and-conquer strategy, decomposing the computational domain into hierarchical units with varying cell sizes. James’s algorithm is used to compute the zero-boundary potentials of lower-level units, which are systematically integrated to reconstruct the zero-boundary potential over the entire domain. These calculations are performed efficiently via matrix-vector operations using various precomputed kernel matrices. The open-boundary potential is then obtained by applying a discrete Green’s function to the effective screening density induced at the domain boundaries. The overall algorithm achieves a computational complexity of O ( N 3 log N ) , where N denotes the number of cells in one dimension. We implement the solver in the FARGO3D magnetohydrodynamics code and demonstrate its performance and second-order accuracy through a series of test problems.

Source: The Astrophysical Journal Supplement Series

DOI: 10.3847/1538-4365/adec68

Authors: Jeonghyeon Ahn, Woong-Tae Kim, Yonghwi Kim

Institutions: Seoul National University, Korea Institute of Science & Technology Information

Language: English

Topic: Electromagnetic Scattering and Analysis

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $4,499

Funders: Korea Institute of Science and Technology Information, National Research Foundation of Korea