Paper Info
Title
AMG PRECONDITIONERS FOR LINEAR SOLVERS TOWARDS EXTREME SCALE
Abstract
Linear solvers for large and sparse systems are a key element of scientific applications, and their efficient implementation is necessary to harness the computational power of current computers. Algebraic MultiGrid (AMG) preconditioners are a popular ingredient of such linear solvers; this is the motivation for the present work, where we examine some recent developments in a package of AMG preconditioners to improve efficiency, scalability, and robustness on extreme scale problems. The main novelty is the design and implementation of a parallel coarsening algorithm based on aggregation of unknowns employing weighted graph matching techniques; this is a completely automated procedure, requiring no information from the user, and applicable to general symmetric positive definite (s.p.d.) matrices. The new coarsening algorithm improves in terms of numerical scalability at low operator complexity upon decoupled aggregation algorithms available in previous releases of the package. The preconditioners package is built on the parallel software framework PSBLAS, which has also been updated to progress towards exascale. We present weak scalability results on one of the most powerful supercomputers in Europe for linear systems with sizes up to O(10(10)) unknowns.
Year
DOI
Venue
2021
10.1137/20M134914X
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
DocType
Volume
algebraic multigrid, preconditioners, parallel scalability
Journal
43
Issue
ISSN
Citations 
5
1064-8275
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Pasqua D'Ambra100.34
Fabio Durastante200.34
Salvatore Filippone321227.56