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AMG based on compatible weighted matching for GPUs. (arXiv:1810.04221v1 [math.NA])
来源于:arXiv
We describe main issues and design principles of an efficient implementation,
tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of
an Algebraic Multigrid (AMG) preconditioner previously proposed by one of the
authors and already available in the open-source package BootCMatch: Bootstrap
algebraic multigrid based on Compatible weighted Matching for standard CPU. The
AMG method relies on a new approach for coarsening sparse symmetric positive
definite (spd) matrices, named "coarsening based on compatible weighted
matching". It exploits maximum weight matching in the adjacency graph of the
sparse matrix, driven by the principle of compatible relaxation, providing a
suitable aggregation of unknowns which goes beyond the limits of the usual
heuristics applied in the current methods. We adopt an approximate solution of
the maximum weight matching problem, based on a recently proposed parallel
algorithm, referred as the Suitor algorithm, and show that it allow us to
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