Issue |
A&A
Volume 671, March 2023
|
|
---|---|---|
Article Number | A81 | |
Number of page(s) | 15 | |
Section | Numerical methods and codes | |
DOI | https://doi.org/10.1051/0004-6361/202244701 | |
Published online | 08 March 2023 |
Computing the gravitational potential on nested meshes using the convolution method★
1
University of Vienna, Department of Astrophysics,
Türkenschanzstrasse 17,
Vienna
1180, Austria
e-mail: eduard.vorobiev@univie.ac.at
2
Institute of Computational Mathematics and Mathematical Geophysics SB RAS,
Lavrentieva ave., 6,
Novosibirsk
630090, Russia
3
Research Institute of Physics, Southern Federal University,
Stachki Ave. 194,
Rostov-on-Don
344090, Russia
4
School of Physics, University of Leicester,
Leicester,
LE1 7RH, UK
Received:
5
August
2022
Accepted:
6
January
2023
Aims. Our aim is to derive a fast and accurate method for computing the gravitational potential of astrophysical objects with high contrasts in density, for which nested or adaptive meshes are required.
Methods. We present an extension of the convolution method for computing the gravitational potential to the nested Cartesian grids. The method makes use of the convolution theorem to compute the gravitational potential using its integral form.
Results. A comparison of our method with the iterative outside-in conjugate gradient and generalized minimal residual methods for solving the Poisson equation using nonspherically symmetric density configurations has shown a comparable performance in terms of the errors relative to the analytic solutions. However, the convolution method is characterized by several advantages and outperforms the considered iterative methods by factors 10–200 in terms of the runtime, especially when graphics processor units are utilized. The convolution method also shows an overall second-order convergence, except for the errors at the grid interfaces where the convergence is linear.
Conclusions. High computational speed and ease in implementation can make the convolution method a preferred choice when using a large number of nested grids. The convolution method, however, becomes more computationally costly if the dipole moments of tightly spaced gravitating objects are to be considered at coarser grids.
Key words: methods: numerical / gravitation / hydrodynamics
Code can be viewed at https://github.com/jamesmckevitt/CM4NG
The Authors 2023
Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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