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

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.

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