# A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM

## TL;DR

This paper introduces a flexible, parallel geometric multigrid method for finite element analysis on adaptively refined meshes, optimized for high-performance computing environments.

## Contribution

It presents a novel adaptive multigrid algorithm with local smoothing and space-filling curve partitioning, implemented in the deal.II library for improved parallel efficiency.

## Key findings

- Model of mesh hierarchy distribution efficiency
- Comparison of model predictions with runtime measurements
- Implementation in the deal.II library

## Abstract

We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by using a space filling curve for the leaf mesh and distributing ancestors in the hierarchy based on the leaves. We present a model of the efficiency of mesh hierarchy distribution and compare its predictions to runtime measurements. The algorithm is implemented as part of the deal.II finite element library and as such available to the public.