Abstract In this paper, a distributed parallel version of algebraic multigrid method is proposed for linear algebraic systems arising from discretization of systems of scalar elliptic equations. The implementation demonstrates good scalability on thousands of cores and surpasses the open source packages HYPRE BoomerAMG and PETSc GAMG in performance on a number of systems. Effective scalable implementations of algorithms in the setup stage of the algebraic multigrid method are considered. The possibility of reducing the number of processors in communicator for coarse systems has been implemented. Variants of cycles of the multigrid method are considered, which make it possible to obtain independence of the number of iterations as the system size increases without losing the scalability of the method. These developments form the basis for further extension of the method for multiphysical problems.
Konshin et al. (2026) studied this question.
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