# A robust adaptive algebraic multigrid linear solver for structural mechanics

## TL;DR

This paper introduces a robust adaptive algebraic multigrid solver tailored for large-scale structural mechanics problems, demonstrating improved efficiency and robustness over existing methods through extensive numerical testing.

## Contribution

The work presents a novel adaptive AMG method that enhances usability and efficiency for solving large structural mechanics linear systems, outperforming current state-of-the-art solvers.

## Key findings

- Successfully solves large problems with millions of unknowns
- Demonstrates superior robustness and efficiency
- Outperforms existing linear solvers in tests

## Abstract

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming kernel in commercial simulators; thus, it is of significant interest the development of robust and efficient linear solvers for such applications. In this context, direct solvers, which are based on LU factorization techniques, are often used due to their robustness and easy setup; however, they can reach only superlinear complexity, in the best case, thus, have limited applicability depending on the problem size. On the other hand, iterative solvers based on algebraic multigrid (AMG) preconditioners can reach up to linear complexity for sufficiently regular problems but do not always converge and require more knowledge from the user for an efficient setup. In this work, we present an adaptive AMG method specifically designed to improve its usability and efficiency in the solution of structural problems. We show numerical results for several practical applications with millions of unknowns and compare our method with two state-of-the-art linear solvers proving its efficiency and robustness.