自顶向下聚集型代数多重网格预条件的健壮性与参数敏感性研究

Research of robustness and parameter-sensitivity of aggregation based algebraic multigrid preconditioner from top to bottom

针对自顶向下聚集型代数多重网格预条件,首先对问题规模敏感性进行了研究,并与基于强连接的经典聚集型算法进行了系统比较,发现大部分情况下,该算法具有明显优势,特别是在采用Jacobi光滑时优势更显著;之后,对最粗网格层的分割数与每次每个子图进行分割时的分割数这两个参数进行了敏感性分析。综合分析表明,自顶向下聚集型代数多重网格预条件具有较好的健壮性,特别是在采用Gauss-Seidel光滑,或采用九点差分离散时,健壮性表现更加充分。

For the aggregation based algebraic multigrid preconditioner from top to bottom,this paper investigated the sensitivity to the scale of the problem first and compared to the classical aggregation schemes based on strong connections systematically.The results show that this algorithm is superior in the most cases.When Jacobi smoothing is used,the privileges is more significant.Then it investigated the sensitivity to two parameters,including the number of partitions in the coarsest level and that for each sub-graph.The systematic analyses show that the aggregation based algebraic multigrid preconditioner from top to bottom is robust and when Gauss-Seidel smoothing is used or the nine-point difference scheme is used,the robustness is more sufficient.