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

Serge Gratton(gratton***at***cerfacs.fr)
Philippe Toint(philippe.toint***at***fundp.ac.be)
Jean Tshimanga Ilunga(jtshimanga***at***serviware.com)

Abstract: This paper 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.

Keywords: Covariance matrix; Correlation; Difusion equation; Conjugate Gradient; Multigrid; Data Assimilation

Category 1: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Category 2: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Citation:

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Entry Submitted: 09/09/2012
Entry Accepted: 09/09/2012
Entry Last Modified: 09/09/2012

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