  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.

Instrumentation and Methods for Astrophysics