# Improving Solve Time of aggregation-based adaptive AMG

## TL;DR

This paper enhances the solve time of a bootstrap algebraic multigrid (AMG) method by integrating smooth vectors into a single hierarchy with larger aggregates, leading to faster convergence and reduced memory usage.

## Contribution

The authors introduce a novel approach to incorporate algebraically smooth vectors into a unified hierarchy using larger aggregates, improving AMG performance.

## Key findings

- Significant reduction in solve time and memory usage.
- Good convergence properties of the modified AMG.
- Effective on complex PDE discretizations in 2D and 3D.

## Abstract

This paper proposes improving the solve time of a bootstrap AMG designed previously by the authors. This is achieved by incorporating the information, set of algebraically smooth vectors, generated by the bootstrap algorithm, in a single hierarchy by using sufficiently large aggregates, and these aggregates are compositions of aggregates already built throughout the bootstrap algorithm. The modified AMG method has good convergence properties and shows significant reduction in both, memory and solve time. These savings with respect to the original bootstrap AMG are illustrated on some difficult (for standard AMG) linear systems arising from discretization of scalar and vector function elliptic partial differential equations (PDEs) in both 2d and 3d.