Conjugate gradients versus multigrid solvers for diffusion-based correlation models in data assimilation

S. Gratton, P. L. Toint, J. Tshimanga

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Abstract

This article provides a theoretical and experimental comparison between conjugate gradients and multigrid, two iterative schemes for solving linear systems, in the context of applying diffusion-based correlation models in data assimilation. In this context, a large number of such systems has to be (approximately) solved if the implicit mode is chosen for integrating the involved diffusion equation over pseudo-time, thereby making their efficient handling crucial for practical performance. It is shown that the multigrid approach has a significant advantage, especially for larger correlation lengths and/or large problem sizes.

Original languageEnglish
Pages (from-to)1481-1487
Number of pages7
JournalQuarterly Journal of the Royal Meteorological Society
Volume139
Issue number675
DOIs
Publication statusPublished - 2013

Keywords

  • 4D-Var
  • Covariance design
  • Iterative method
  • Linear system

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