A 2D climate energy balance model coupled with a 3D deep ocean model.
A bifurcation result for Sturm-Liouville problems with a set-valued term.
A brief introduction to spatio-temporal modelling.
A comparison of approaches for the construction of reduced basis for stochastic Galerkin matrix equations
We examine different approaches to an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with different, uncertain coefficients in apriori known subdomains. The solution of the SG system of equations is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks for a low-rank representation of the solution. The construction of the RB is usually done iteratively...
A comparison of deterministic and Bayesian inverse with application in micromechanics
The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities...
A comparison of multilevel adaptive methods for hurricane track prediction.
A comparison of the accuracy of the finite-difference solution to boundary value problems for the Helmholtz equation obtained by direct and iterative methods
The development of iterative methods for solving linear algebraic equations has brought the question of when the employment of these methods is more advantageous than the use of the direct ones. In the paper, a comparison of the direct and iterative methods is attempted. The methods are applied to solving a certain class of boundary-value problems for elliptic partial differential equations which are used for the numerical modeling of electromagnetic fields in geophysics. The numerical experiments...
A discrete wavelet analysis of freak waves in the ocean.
A dual data assimilation method for a layered quasi-geostrophic ocean model.
In this paper we introduce the equations of a layered quasi-geostrophic ocean model, and the corresponding data assimilation problem. We first give the variational formulation. We then point out the linear theory of duality. Finally, we apply duality to our nonlinear model by describing an algorithm to solve the data assimilation problem, introducing a dual cost function and a simple way to compute its gradient.
A generalized 2-D Poincaré inequality.
A method for solving a boundary value problem for a partial differential equation of elliptic type.
A new approach to the problem of removal of soluble gaseous pollutants from the atmosphere and its correspondence with the existing approach.
A new numerical model for propagation of tsunami waves
A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model.
A new two-dimensional shallow water model including pressure effects and slow varying bottom topography
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...
A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...
A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.
We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...
A nonnegatively constrained trust region algorithm for the restoration of images with an unknown blur.
A note on a degenerate elliptic equation with applications for lakes and seas.
A novel approach to modelling of flow in fractured porous medium
There are many problems of groundwater flow in a disrupted rock massifs that should be modelled using numerical models. It can be done via “standard approaches” such as increase of the permeability of the porous medium to account the fracture system (or double-porosity models), or discrete stochastic fracture network models. Both of these approaches appear to have their constraints and limitations, which make them unsuitable for the large- scale long-time hydrogeological calculations. In the article,...
A null controllability data assimilation methodology applied to a large scale ocean circulation model
Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, C. R. Math. Acad. Sci. Paris 335 (2002) 161–166] and [Puel, SIAM J. Control Optim. 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final...