Convergent analysis of algebraic multigrid method with data-driven parameter learning for non-selfadjoint elliptic problems

TL;DR

This paper enhances algebraic multigrid methods for non-selfadjoint elliptic problems by integrating data-driven Gaussian process regression to optimize parameters, improving efficiency and convergence.

Contribution

It introduces a novel combination of GADI-HS iteration with data-driven parameter learning via GPR for AMG, with proven convergence and improved performance.

Findings

GPR accurately predicts optimal parameters

Significant reduction in computational time

Effective convergence of the proposed method

Abstract

In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and introduce a data-driven parameter learing method called Gaussian process regression (GPR) to predict optimal parameters. Numerical experimental results show that using GPR to predict parameters can save a significant amount of time cost and approach the optimal parameters accurately.