# A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC

## TL;DR

This paper introduces an efficient MPI-parallel geometric multigrid library designed for quadtree and octree adaptive mesh refinement grids, supporting various geometries and boundary conditions, and demonstrates its application in magnetohydrodynamic simulations.

## Contribution

We developed a scalable multigrid library for AMR grids that integrates with MPI-AMRVAC, enabling efficient elliptic solves in complex geometries.

## Key findings

- Scales up to 1792 cores with good performance.
- Supports multiple boundary conditions including free-space for 3D Poisson.
- Effectively controls magnetic divergence in MHD simulations.

## Abstract

We present an efficient MPI-parallel geometric multigrid library for quadtree (2D) or octree (3D) grids with adaptive refinement. Cartesian 2D/3D and cylindrical 2D geometries are supported, with second-order discretizations for the elliptic operators. Periodic, Dirichlet, and Neumann boundary conditions can be handled, as well as free-space boundary conditions for 3D Poisson problems, for which we use an FFT-based solver on the coarse grid. Scaling results up to 1792 cores are presented. The library can be used to extend adaptive mesh refinement frameworks with an elliptic solver, which we demonstrate by coupling it to MPI-AMRVAC. Several test cases are presented in which the multigrid routines are used to control the divergence of the magnetic field in magnetohydrodynamic simulations.