English

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

Numerical Analysis 2025-12-08 v3 Numerical Analysis Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.2410.23681,
  title  = {Convergent analysis of algebraic multigrid method with data-driven parameter learning for non-selfadjoint elliptic problems},
  author = {Juan Zhang and Junyue Luo},
  journal= {arXiv preprint arXiv:2410.23681},
  year   = {2025}
}

Comments

The main theoretical development of this manuscript is presented in Section 2, which contains the following errors: The manuscript addresses non-self-adjoint elliptic problems, the restriction operator $R$ is not the transpose of the interpolation operator $P$. However, the manuscript denotes the smoother as $R_{k}$, a notation that may lead to conceptual confusion

R2 v1 2026-06-28T19:42:28.244Z