Low rank updates in preconditioning the saddle point systems arising from data assimilation problems

The numerical solution of saddle point systems has received a lot of attention over the past few years in a wide variety of applications such as constrained optimization, computational fluid dynamics and optimal control, to name a few. In this paper, we focus on the saddle point formulation of a large-scale variational data assimilation problem, where the computations involving the constraint blocks are supposed to be much more expensive than those related to the (1, 1) block of the saddle point matrix. New low-rank limited memory preconditioners exploiting the particular structure of the problem are proposed and analysed theoretically. Numerical experiments performed within the Object-Oriented Prediction System are presented to highlight the relevance of the proposed preconditioners

Magnetization of densely packed interacting magnetic nanoparticles with cubic and uniaxial anisotropies: A Monte Carlo study

International audienceThe magnetization curves of densely packed single domain magnetic nanoparticles (MNP) are investigated by Monte Carlo simulations in the framework of an effective one spin model. The particles whose size polydispersity is taken into account are arranged in spherical clusters and both dipole dipole interactions (DDI) and magnetic anisotropy energy (MAE) are included in the total energy. Having in mind the special case of spinel ferrites of intrinsic cubic symmetry, combined cubic and uniaxial magnetocrystalline anisotropies are considered with different configurations for the orientations of the cubic and uniaxial axes. It is found that the DDI, together with a marked reduction of the linear susceptibility are responsible for a damping of the peculiarities due to the MAE cubic component on the magnetization. As an application, we show that the simulated magnetization curves compare well to experimental results for $\gamma$--Fe$_2$O$_3$ MNP for small to moderate values of the field

Coupling dynamic equations and satellite images for modelling ocean surface circulation

International audienceSatellite image sequences visualise the ocean surface and allow assessing its dynamics. Processing these data is then of major interest to get a better understanding of the observed processes. As demonstrated by state-of-the-art, image assimilation permits to retrieve surface motion, based on assumptions on the dynamics. In this paper, we demonstrate that a simple heuristics, such as the Lagrangian constancy of velocity, can be used and successfully replaces the complex physical properties described by the Navier-Stokes equations for assessing surface circulation from satellite images. A data assimilation method is proposed that adds an acceleration term a(t) to this Lagrangian constancy equation, which summarises all physical processes other than advection. A cost function is designed that quantifies discrepancy between satellite data and model values. This cost function is minimised by the BFGS solver with a dual method of data assimilation. The result is the initial motion field and the acceleration terms a(t) on the whole temporal interval. These values a(t) model the forces, other than advection, that contribute to surface circulation. Our approach was tested on synthetic data and with Sea Surface Temperature images acquired on Black Sea. Results are quantified and compared to those of state-of-the-art methods