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.
翻译:提议对平滑聚合代数多格(SA-AMG)方法进行四项调整,目的是在离散矩阵包含许多薄弱连接的情况下,提高求解器的趋同性和稳健性,这些薄弱连接可导致粗粗离散矩阵内的填充量高于预期水平,还可能导致在延长的平滑阶段内出现最不理想的平滑。这些平稳退步是由于在放弃薄弱连接后过滤的矩阵内某些二进制分解条目的大小相对较小。新的算法考虑对界定延展器滑动器的雅各比式步骤进行修改,对过滤式矩阵进行修改,并对由此产生的电网转移操作者进行直接修改。