The Athena++ Adaptive Mesh Refinement Framework: Multigrid Solvers for Self-Gravity

TL;DR

This paper introduces multigrid solvers integrated into the Athena++ AMR framework for efficient and accurate self-gravity calculations, demonstrating superior performance over FFT-based methods and applying it to protostellar collapse simulations.

Contribution

The paper presents the implementation of multigrid solvers within Athena++'s AMR framework, enabling efficient self-gravity solutions with various boundary conditions and hybrid parallelization.

Findings

Multigrid outperforms FFT-based methods in accuracy and speed.

The solvers scale well on parallel architectures.

Application to protostellar collapse demonstrates practical utility.

Abstract

We describe the implementation of multigrid solvers in the Athena++ adaptive mesh refinement (AMR) framework and their application to the solution of the Poisson equation for self-gravity. The new solvers are built on top of the AMR hierarchy and TaskList framework of Athena++ for efficient parallelization. We adopt a conservative formulation for the Laplacian operator that avoids artificial accelerations at level boundaries. Periodic, fixed, and zero-gradient boundary conditions are implemented, as well as open boundary conditions based on a multipole expansion. Hybrid parallelization using both MPI and OpenMP is adopted, and we present results of tests demonstrating the accuracy and scaling of the methods. On a uniform grid we show multigrid significantly outperforms methods based on FFTs, and requires only a small fraction of the compute time required by the (highly optimized) magnetohydrodynamic solver in Athena++. As a demonstration of the capabilities of the methods, we present the results of a test calculation of magnetized protostellar collapse on an adaptive mesh.