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A New Class of AMG Interpolation Methods Based on Matrix-Matrix Multiplications
SIAM Journal on Scientific Computing ( IF 3.1 ) Pub Date : 2021-07-19 , DOI: 10.1137/20m134931x
Ruipeng Li , Björn Sjögreen , Ulrike Meier Yang

SIAM Journal on Scientific Computing, Ahead of Print.
A new class of distance-two interpolation methods for algebraic multigrid (AMG) that can be formulated in terms of sparse matrix-matrix multiplications is presented and analyzed. Compared with similar distance-two prolongation operators [H. De Sterck et al., Numer. Linear Algebra Appl., 15 (2008), pp. 115--139], the proposed algorithms exhibit improved efficiency and portability to various computing platforms, since they allow one to easily exploit existing high-performance sparse matrix kernels. The new interpolation methods have been implemented in hypre [R. D. Falgout and U. M. Yang, hypre: A library of high performance preconditioners, in Computational Science --- ICCS 2002, P. M. A. Sloot et al., eds., Springer, Berlin, Heidelberg, 2002, pp. 632--641], a widely used parallel multigrid solver library. With the proposed interpolations, the overall time of hypre's BoomerAMG setup can be considerably reduced, while sustaining equivalent, sometimes improved, convergence rates. Numerical results for a variety of test problems on parallel machines are presented that support the superiority of the proposed interpolation operators over the existing ones in hypre.


中文翻译:

一类新的基于矩阵-矩阵乘法的 AMG 插值方法

SIAM 科学计算杂志,提前印刷。
提出并分析了一类新的用于代数多重网格 (AMG) 的距离二插值方法,该方法可以根据稀疏矩阵-矩阵乘法来制定。与相似距离-二延拓算子相比[H. De Sterck 等人,Numer。Linear Algebra Appl., 15 (2008), pp. 115--139],所提出的算法展示了改进的效率和对各种计算平台的可移植性,因为它们允许人们轻松利用现有的高性能稀疏矩阵内核。新的插值方法已在 hypre [RD Falgout 和 UM Yang, hypre: A library of high performance preconditioners, in Computational Science --- ICCS 2002, PMA Sloot et al., eds., Springer, Berlin, Heidelberg, 2002 , pp. 632--641],一个广泛使用的并行多重网格求解器库。使用建议的插值,hypre 的 BoomerAMG 设置的总时间可以大大减少,同时保持等效的、有时会提高的收敛速度。给出了并行机上各种测试问题的数值结果,支持所提出的插值算子优于 hypre 中现有的插值算子。
更新日期:2021-07-20
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