# Afivo: a framework for quadtree/octree AMR with shared-memory parallelization and geometric multigrid methods

## TL;DR

Afivo is a simple, shared-memory framework for adaptive mesh refinement in 2D and 3D, featuring a geometric multigrid solver, suitable for large-scale elliptic PDE simulations on single nodes.

## Contribution

It introduces a lightweight, easy-to-modify framework for AMR with integrated multigrid methods and shared-memory parallelism, optimized for desktop and workstation use.

## Key findings

- Efficiently simulates up to 10^8 unknowns on single nodes.
- Successfully used for large 3D streamer discharge simulations.
- Provides flexible, user-implementable physics modules.

## Abstract

Afivo is a framework for simulations with adaptive mesh refinement (AMR) on quadtree (2D) and octree (3D) grids. The framework comes with a geometric multigrid solver, shared-memory (OpenMP) parallelism and it supports output in Silo and VTK file formats. Afivo can be used to efficiently simulate AMR problems with up to about $10^{8}$ unknowns on desktops, workstations or single compute nodes. For larger problems, existing distributed-memory frameworks are better suited. The framework has no built-in functionality for specific physics applications, so users have to implement their own numerical methods. The included multigrid solver can be used to efficiently solve elliptic partial differential equations such as Poisson's equation. Afivo's design was kept simple, which in combination with the shared-memory parallelism facilitates modification and experimentation with AMR algorithms. The framework was already used to perform 3D simulations of streamer discharges, which required tens of millions of cells.