Conjugate gradients versus multigrid solvers for diffusion‐based correlation models in data assimilation. (4th January 2013) - Gratton, S.; Toint, P. L.; Tshimanga, J.
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.