Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. I: Block Jacobi diagonalization

Wenwu Chen, Bill Poirier

Research output: Contribution to journalArticlepeer-review

22 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 [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 I) emphasizes construction of the block Jacobi preconditioner matrices. This is achieved in a preprocessing step, performed prior to the subsequent iterative linear solve step, considered in a companion paper (paper II). Results indicate that the block Jacobi routines scale remarkably well on parallel computing platforms, and should remain effective over tens of thousands of nodes.

Original languageEnglish
Pages (from-to)185-197
Number of pages13
JournalJournal of Computational Physics
Volume219
Issue number1
DOIs
StatePublished - Nov 20 2006

Keywords

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

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