On the parallel iterative solution of linear systems arising in the FEAST algorithm for computing inner eigenvalues

Martin Galgon, Lukas Krämer, Jonas Thies, Achim Basermann, Bruno Lang

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)

Abstract

Methods for the solution of sparse eigenvalue problems that are based on spectral projectors and contour integration have recently attracted more and more attention. Such methods require the solution of many shifted sparse linear systems of full size. In most of the literature concerning these eigenvalue solvers, only few words are said on the solution of the linear systems, but they turn out to be very hard to solve by iterative linear solvers in practice. In this work we identify a row projection method for the solution of the inner linear systems encountered in the FEAST algorithm and introduce a novel hybrid parallel and fully iterative implementation of the eigenvalue solver. Our approach ultimately aims at achieving extreme parallelism by exploiting the algorithm's potential on several levels. We present numerical examples where graphene modeling is one of the target applications. In this application, several hundred or even thousands of eigenvalues from the interior of the spectrum are required, which is a big challenge for state-of-the-art numerical methods.

Original languageEnglish
Pages (from-to)153-163
Number of pages11
JournalParallel Computing
Volume49
DOIs
Publication statusPublished - 1 Nov 2015
Externally publishedYes

Keywords

  • CARP-CG
  • FEAST
  • Graphene modeling
  • Multi-coloring
  • Parallel inner eigenvalue computation
  • Sparse linear systems

Fingerprint Dive into the research topics of 'On the parallel iterative solution of linear systems arising in the FEAST algorithm for computing inner eigenvalues'. Together they form a unique fingerprint.

Cite this