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

               S. Gratton, Ph. L. Toint, J. Tshimanga Ilunga
                             Report naXys-14-2012


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.