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.

翻译：本文采用实用GADI-HS迭代作为求解二阶非自伴椭圆问题的代数多重网格（AMG）方法中的光滑子。此外，我们证明了所推导算法的收敛性，并引入一种称为高斯过程回归（GPR）的数据驱动参数学习方法以预测最优参数。数值实验结果表明，使用GPR预测参数可显著节省时间成本，并能精确逼近最优参数。