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A New Shifted Block GMRES Method with Inexact Breakdowns for Solving Multi-Shifted and Multiple Right-Hand Sides Linear Systems

Sun, D-L., Huang, T-Z., Carpentieri, B. & Jing, Y-F., 15-Feb-2019, In : Journal of scientific computing. 78, 2, p. 746-769 24 p.

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  • A New Shifted Block GMRES Method with Inexact Breakdowns for Solving Multi-Shifted and Multiple Right-Hand Sides Linear Systems

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DOI

  • Dong-Lin Sun
  • Ting-Zhu Huang
  • Bruno Carpentieri
  • Yan-Fei Jing

We consider the efficient solution of linear systems with multiple shifts and multiple right-hand sides given simultaneously that arise frequently in large-scale scientific and engineering simulations. We introduce a new shifted block GMRES method that can solve the whole sequence of linear systems simultaneously, it handles effectively the situation of inexact breakdowns in the inner block Arnoldi procedure for improved robustness, and recycles spectral information at restart to achieve faster convergence. Numerical experiments are reported on a suite of sparse matrix problems and in realistic quantum chromodynamics application to show the potential of the new proposed method to solve general multi-shifted and multiple right-hand sides linear systems fast and efficiently.

Original languageEnglish
Pages (from-to)746-769
Number of pages24
JournalJournal of scientific computing
Volume78
Issue number2
Publication statusPublished - 15-Feb-2019

    Keywords

  • Shifted block Krylov subspace methods, Deflated restarting, Inexact breakdowns, Preconditioning techniques, RESTARTED GMRES, DEFLATION, ALGORITHM, VARIANTS, PAGERANK

ID: 118805432