困难拉伸网格和变系数问题的光滑集结
Smooth Aggregation for Difficult Stretched Mesh and Coefficient Variation Problems
摘要：
四个适应的平滑聚合代数多重网格（SA-AMG）方法提出了一个眼睛对提高求解器的收敛性和鲁棒性的情况下，离散矩阵包含许多弱连接。这些弱连接可能导致粗离散化矩阵内的填充水平高于预期水平，并且还可能导致离散化器平滑阶段内的次优平滑。这些平滑缺点是由于在丢弃弱连接之后获得的过滤矩阵内的一些对角条目的相对小的大小。新的算法考虑修改的Jacobi样的步骤，定义了平滑，修改的过滤矩阵，并直接修改所得到的网格传输操作。数值结果表明所提出的适应的潜在好处。
英文摘要：
Four adaptations of the smoothed aggregation algebraic multigrid (SA-AMG) method are proposed with an eye towards improving the convergence and robustness of the solver in situations when the discretization matrix contains many weak connections. These weak connections can cause higher than expected levels of fill-in within the coarse discretization matrices and can also give rise to sub-optimal smoothing within the prolongator smoothing phase. These smoothing drawbacks are due to the relatively small size of some diagonal entries within the filtered matrix that one obtains after dropping the weak connections. The new algorithms consider modifications to the Jacobi-like step that defines the prolongator smoother, modifications to the filtered matrix, and also direct modifications to the resulting grid transfer operators. Numerical results are given illustrating the potential benefits of the proposed adaptations.
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