# High-performance dune modules for solving large-scale, strongly anisotropic elliptic problems with applications to aerospace composites

## TL;DR

This paper introduces a high-performance, open-source iterative solver integrated into dune-pdelab for large-scale, anisotropic elliptic PDEs, significantly advancing aerospace composite simulations and other large-scale applications.

## Contribution

It presents a scalable, robust two-level additive Schwarz preconditioner within dune-composites, enabling efficient solutions of large anisotropic elliptic problems on supercomputers.

## Key findings

- Solver scales to over 15,000 cores
- Successfully solves aerospace composite problems with 200 million degrees of freedom
- Demonstrates robustness on subsurface flow benchmark

## Abstract

The key innovation in this paper is an open-source, high-performance iterative solver for high contrast, strongly anisotropic elliptic partial differential equations implemented within dune-pdelab. The iterative solver exploits a robust, scalable two-level additive Schwarz preconditioner, GenEO (Spillane et al. 2014). The development of this solver has been motivated by the need to overcome the limitations of commercially available modeling tools for solving structural analysis simulations in aerospace composite applications. Our software toolbox dune-composites encapsulates the mathematical complexities of the underlying packages within an efficient C++ framework, providing an application interface to our new high-performance solver. We illustrate its use on a range of industrially motivated examples, which should enable other scientists to build on and extend dune-composites and the GenEO preconditioner for use in their own applications. We demonstrate the scalability of the solver on more than 15,000 cores of the UK national supercomputer Archer, solving an aerospace composite problem with over 200 million degrees of freedom in a few minutes. This scale of computation brings composites problems that would otherwise be unthinkable into the feasible range. To demonstrate the wider applicability of the new solver, we also confirm the robustness and scalability of the solver on SPE10, a challenging benchmark in subsurface flow/reservoir simulation.