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A New Class of AMG Interpolation Methods Based on Matrix-Matrix Multiplications
SIAM Journal on Scientific Computing  (IF2.373),  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.