Application of graph theory in algebraic multigrid methods for solving sparse SLAES

In this paper, we discuss geometric and algebraic multigrid methods, graph coarsening algorithms, and metrics used to construct vertex aggregations. A coarsening method based on A. Napov and Y. Notey’s criterion is implemented. Gustavson’s algorithms for efficient multiplication and transposition of matrices in CSR format are used for computation time optimization, which allowed to process graphs with more than one million vertices. The purpose of the presented work is to develop a data structure and computational environment components for high-performance solution of a wide class of SLAEs.