Relaxed RS0 or CLJP coarsening strategy for parallel AMG

Abstract

Algebraic multigrid (AMG) algorithm is well known for it efficiencies in solving of larger scale sparse linear systems arising from the computationally challenging applications especially on unstructured or deformed structured grid. Though most of its components can be parallelized in a straightforward way, the classical coarsening process such as the Ruge–Stüben (RS) strategy is highly sequential and requires new parallel approaches. In recent years, many parallel coarsening strategies are presented towards running efficiently on hundreds or thousands of processors. This paper presents two new parallel coarsening strategies towards more efficiently distributing C-points for smaller operator complexity and more robust convergence of iterations. The main idea of these strategies is to smartly synchronize processors for the well-known RS0 or CLJP strategies during the process of coarsening. Qualitative analyses and numerical experiments show that our new strategies always perform better performance not only for faster convergence but also for smaller operator complexity if we compare them with the currently well-known parallel coarsening strategies such as RS3, Falgout or CLJP using hundreds of processors.