# A High-Performance Implementation of a Robust Preconditioner for Heterogeneous Problems

## TL;DR

This paper introduces an efficient, scalable implementation of the GenEO preconditioner within the DUNE framework, demonstrating its robustness and high performance on large, complex industrial problems with over 200 million degrees of freedom.

## Contribution

It presents a high-performance, scalable implementation of the GenEO preconditioner, showcasing its effectiveness on large-scale heterogeneous problems and providing detailed technical insights.

## Key findings

- Successfully scaled to over 15,000 cores
- Maintains effectiveness on complex parameter distributions
- Outperforms established methods in intractable scenarios

## Abstract

We present an efficient implementation of the highly robust and scalable GenEO preconditioner in the high-performance PDE framework DUNE. The GenEO coarse space is constructed by combining low energy solutions of a local generalised eigenproblem using a partition of unity. In this paper we demonstrate both weak and strong scaling for the GenEO solver on over 15,000 cores by solving an industrially motivated problem with over 200 million degrees of freedom. Further, we show that for highly complex parameter distributions arising in certain real-world applications, established methods become intractable while GenEO remains fully effective. The purpose of this paper is two-fold: to demonstrate the robustness and high parallel efficiency of the solver and to document the technical details that are crucial to the efficiency of the code.