Aggregation based on graph matching and inexact coarse grid solve for algebraic multigrid

TL;DR

This paper introduces a graph matching-based aggregation method for algebraic multigrid that improves robustness and efficiency, especially for highly discontinuous convection diffusion problems, by analyzing the effects of inexact coarse grid solves.

Contribution

It proposes a novel aggregation strategy using graph matching and evaluates the impact of inexact coarse grid solves, demonstrating enhanced robustness over classical AMG methods.

Findings

More robust convergence for discontinuous convection diffusion problems

Effective aggregation via graph matching improves multigrid performance

Inexact coarse grid solves do not significantly degrade convergence

Abstract

A graph based matching is used to construct aggregation for algebraic multigrid. Effects of inexact coarse grid solve is analyzed numerically for a highly discontinuous convection diffusion coefficient matrix and problems from Florida matrix market collection. The proposed strategy is found to be more robust compared to a classical AMG approach.