Efficient solution of 3D elasticity problems with smoothed aggregation algebraic multigrid and block arithmetics

TL;DR

This paper enhances 3D elasticity problem solvers by integrating block arithmetics into smoothed aggregation algebraic multigrid, leading to significant speed and memory improvements in practical applications.

Contribution

It introduces practical methods to incorporate block arithmetics into smoothed aggregation algebraic multigrid, improving efficiency and memory usage for elasticity problems.

Findings

Speed up by 50% in real-world models

Reduced memory requirements by 30%

Implementation is straightforward with minimal code changes

Abstract

Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an efficient and robust choice for the solution of linear systems arising from the discretization of elasticity equations. The system matrices on every level of the multigrid hierarchy have block structure, so using block representation and block arithmetics should significantly improve the solver efficiency. However, the tentative prolongation operator construction may only be done using scalar representation. The paper proposes a couple of practical approaches for enabling the use of block arithmetics with smoothed aggregation algebraic multigrid based on the open-source AMGCL library. It is shown on the example of two real-world model problems that the suggested improvements may speed up the solution by 50% and reduce the memory requirements for the preconditioner by 30%. The implementation is straightforward and only requires a minimal amount of code.