Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. II: QMR linear solver

Wenwu Chen, Bill Poirier

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

Linear systems in chemical physics often involve matrices with a certain sparse block structure. These can often be solved very effectively using iterative methods (sequence of matrix-vector products) in conjunction with a block Jacobi preconditioner [B. Poirier, Numer. Linear Algebra Appl. 7 (2000) 715]. In a two-part series, we present an efficient parallel implementation, incorporating several additional refinements. The present study (paper II) indicates that the basic parallel sparse matrix-vector product operation itself is the overall scalability bottleneck, faring much more poorly than the specialized, block Jacobi routines considered in a companion paper (paper I). However, a simple dimensional combination scheme is found to alleviate this difficulty.

Original languageEnglish
Pages (from-to)198-209
Number of pages12
JournalJournal of Computational Physics
Volume219
Issue number1
DOIs
StatePublished - Nov 20 2006

Keywords

  • Chemical physics
  • Eigensolver
  • Linear solver
  • Parallel computing
  • Preconditioning
  • Sparse matrix

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