# Compression challenges in large scale PDE solvers

## TL;DR

This paper reviews the challenges and solutions related to data compression in large-scale PDE solvers, emphasizing the importance of efficient data handling across memory hierarchies to improve computational performance.

## Contribution

It provides a comprehensive survey of data compression techniques tailored for PDE solvers across all memory hierarchy levels, highlighting recent developments and open challenges.

## Key findings

- Compression reduces data transfer bottlenecks in PDE solvers.
- Memory hierarchy-aware compression techniques improve solver efficiency.
- The survey identifies key research directions for future compression methods.

## Abstract

Solvers for partial differential equations (PDE) are one of the cornerstones of computational science. For large problems, they involve huge amounts of data that needs to be stored and transmitted on all levels of the memory hierarchy. Often, bandwidth is the limiting factor due to relatively small arithmetic intensity, and increasingly so due to the growing disparity between computing power and bandwidth. Consequently, data compression techniques have been investigated and tailored towards the specific requirements of PDE solvers during the last decades. This paper surveys data compression challenges and corresponding solution approaches for PDE problems, covering all levels of the memory hierarchy from mass storage up to main memory. Exemplarily, we illustrate concepts at particular methods, and give references to alternatives.