### Abstract

The solution of the Poisson equation is a ubiquitous problem in computational astrophysics. Most notably, the treatment of self-gravitating flows involves the Poisson equation for the gravitational field. In hydrodynamics codes using spherical polar grids, one often resorts to a truncated spherical harmonics expansion for an approximate solution. Here we present a non-iterative method that is similar in spirit, but uses the full set of eigenfunctions of the discretized Laplacian to obtain an exact solution of the discretized Poisson equation. This allows the solver to handle density distributions for which the truncated multipole expansion fails, such as off-center point masses. In 3D, the operation count of the new method is competitive with a naive implementation of the truncated spherical harmonics expansion with N _{ℓ} ≈ 15 multipoles. We also discuss the parallel implementation of the algorithm. The serial code and a template for the parallel solver are made publicly available.

Original language | English |
---|---|

Article number | 43 |

Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Astrophysical Journal |

Volume | 870 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

### Keywords

- gravitation
- methods: numerical

### Cite this

*Astrophysical Journal*,

*870*(1), 1-9. [43]. https://doi.org/10.3847/1538-4357/aaf100

}

*Astrophysical Journal*, vol. 870, no. 1, 43, pp. 1-9. https://doi.org/10.3847/1538-4357/aaf100

**An FFT-based Solution Method for the Poisson Equation on 3D Spherical Polar Grids.** / Müller, Bernhard; Chan, Conrad.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - An FFT-based Solution Method for the Poisson Equation on 3D Spherical Polar Grids

AU - Müller, Bernhard

AU - Chan, Conrad

PY - 2019/1/1

Y1 - 2019/1/1

N2 - The solution of the Poisson equation is a ubiquitous problem in computational astrophysics. Most notably, the treatment of self-gravitating flows involves the Poisson equation for the gravitational field. In hydrodynamics codes using spherical polar grids, one often resorts to a truncated spherical harmonics expansion for an approximate solution. Here we present a non-iterative method that is similar in spirit, but uses the full set of eigenfunctions of the discretized Laplacian to obtain an exact solution of the discretized Poisson equation. This allows the solver to handle density distributions for which the truncated multipole expansion fails, such as off-center point masses. In 3D, the operation count of the new method is competitive with a naive implementation of the truncated spherical harmonics expansion with N ℓ ≈ 15 multipoles. We also discuss the parallel implementation of the algorithm. The serial code and a template for the parallel solver are made publicly available.

AB - The solution of the Poisson equation is a ubiquitous problem in computational astrophysics. Most notably, the treatment of self-gravitating flows involves the Poisson equation for the gravitational field. In hydrodynamics codes using spherical polar grids, one often resorts to a truncated spherical harmonics expansion for an approximate solution. Here we present a non-iterative method that is similar in spirit, but uses the full set of eigenfunctions of the discretized Laplacian to obtain an exact solution of the discretized Poisson equation. This allows the solver to handle density distributions for which the truncated multipole expansion fails, such as off-center point masses. In 3D, the operation count of the new method is competitive with a naive implementation of the truncated spherical harmonics expansion with N ℓ ≈ 15 multipoles. We also discuss the parallel implementation of the algorithm. The serial code and a template for the parallel solver are made publicly available.

KW - gravitation

KW - methods: numerical

UR - http://www.scopus.com/inward/record.url?scp=85059838062&partnerID=8YFLogxK

U2 - 10.3847/1538-4357/aaf100

DO - 10.3847/1538-4357/aaf100

M3 - Article

VL - 870

SP - 1

EP - 9

JO - The Astrophysical Journal

JF - The Astrophysical Journal

SN - 0004-637X

IS - 1

M1 - 43

ER -