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An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

An iterative implementation of the implicit nonlinear filter

Alexandre J. Chorin, Xuemin Tu (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

Implicit sampling is a sampling scheme for particle filters, designed to move particles one-by-one so that they remain in high-probability domains. We present a new derivation of implicit sampling, as well as a new iteration method for solving the resulting algebraic equations.

Analyse mathématique de modèles variationells en simulation pétrolière. Le cas du modèle black-oil pseudo-compositionnel standard isoterme.

Gérard Gagneux, Ann-Marie Lefevere, Monique Madaune-Tort (1989)

Revista Matemática de la Universidad Complutense de Madrid

The aim of the paper is an analytical and numerical approach to the pseudo-compositional black-oil model for simulating a 3-D isothermal constrained polyphasic flow in porous media, taking into account realistic boundary conditions. The handling of the component conservation laws leads to a strongly coupled system including parabolic quasilinear degenerated equations and first-order hyperbolic inequalities: the introduction of unilateral problems arises from the nature of the thermodynamical equilibrium...

Analysis of the hydrostatic approximation in oceanography with compression term

Tomás Chacón Rebollo, Roger Lewandowski, Eliseo Chacón Vera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...

Analysis of the hydrostatic approximation in oceanography with compression term

Tomás Chacón Rebollo, Roger Lewandowski, Eliseo Chacón Vera (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The hydrostatic approximation of the incompressible 3D stationary Navier-Stokes equations is widely used in oceanography and other applied sciences. It appears through a limit process due to the anisotropy of the domain in use, an ocean, and it is usually studied as such. We consider in this paper an equivalent formulation to this hydrostatic approximation that includes Coriolis force and an additional pressure term that comes from taking into account the pressure in the state equation for...

Application of MCMC to change point detection

Jaromír Antoch, David Legát (2008)

Applications of Mathematics

A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler.

Application of splines for determining the velocity characteristic of a medium from a vertical seismic survey

Vladimir Bogdanov, Wladimir Karsten, Valeriy Miroshnichenko, Yuriy Volkov (2013)

Open Mathematics

A method for solving the inverse kinematic problem of determining the velocity characteristic of a medium from a vertical seismic survey, is proposed. It is based on the combined use of the eikonal equation and spline methods of approximation for multivariable functions. The problem is solved by assuming a horizontally stratified medium; no assumptions about the number of layers and their thickness are made. First, using the data of the first arrival times of the seismic signal from several shotpoints,...

Approximation of a nonlinear elliptic problem arising in a non-newtonian fluid flow model in glaciology

Roland Glowinski, Jacques Rappaz (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical results...

Approximation of a nonlinear elliptic problem arising in a non-Newtonian fluid flow model in glaciology

Roland Glowinski, Jacques Rappaz (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary motion of a glacier is given by a non-Newtonian fluid flow model which becomes, in a first two-dimensional approximation, the so-called infinite parallel sided slab model. The approximation of this model is made by a finite element method with piecewise polynomial functions of degree 1. Numerical results...

Baroclinic Kelvin Waves in a Rotating Circular Basin

R. N. Ibragimov (2012)

Mathematical Modelling of Natural Phenomena

A linear, uniformly stratified ocean model is used to investigate propagation of baroclinic Kelvin waves in a cylindrical basin. It is found that smaller wave amplitudes are inherent to higher mode individual terms of the obtained solutions that are also evanescent away of a costal line toward the center of the circular basin. It is also shown that the individual terms if the obtained solutions can be visualized as spinning patterns in rotating stratified fluid confined in a circular basin. Moreover,...

Bayesian methods in hydrology: a review.

David Ríos Insua, Raquel Montes Díez, Jesús Palomo Martínez (2002)

RACSAM

Hydrology and water resources management are inherently affected by uncertainty in many of their involved processes, including inflows, rainfall, water demand, evaporation, etc. Statistics plays, therefore, an essential role in their study. We review here some recent advances within Bayesian statistics and decision analysis which will have a profound impact in these fields.

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