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

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.

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