# Dynamic load balancing for large-scale adaptive finite element computation

## TL;DR

This paper presents dynamic load balancing algorithms for adaptive finite element computations, focusing on efficient grid redistribution to improve partitioning quality and reduce communication overhead in parallel PDE solutions.

## Contribution

It introduces novel dynamic load balancing algorithms specifically designed for adaptive finite element methods and demonstrates their efficiency on the PHG platform.

## Key findings

- Algorithms achieve good partitioning quality.
- Algorithms are efficient in dynamic grid redistribution.
- Numerical experiments validate the effectiveness of the methods.

## Abstract

For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the communications among processes. When calculating the partial differential equations using adaptive finite element methods, the grid and the basis functions adjust in each iteration, which introduce load balancing issues. The grid should be redistributed dynamically. This paper studies dynamic load balancing algorithms and the implementation on the adaptive finite element platform PHG. The numerical experiments show that algorithms studied in this paper have good partitioning quality, and they are efficient.