Displaying similar documents to “Consistent algorithms marching along characteristics for the numerical solution of the Boltzmann equation.”

Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering

Xavier Antoine, Hélène Barucq (2005)

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

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This paper addresses some results on the development of an approximate method for computing the acoustic field scattered by a three-dimensional penetrable object immersed into an incompressible fluid. The basic idea of the method consists in using on-surface differential operators that locally reproduce the interior propagation phenomenon. This approach leads to integral equation formulations with a reduced computational cost compared to standard integral formulations coupling both the...

Coupling of transport and diffusion models in linear transport theory

Guillaume Bal, Yvon Maday (2002)

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

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This paper is concerned with the coupling of two models for the propagation of particles in scattering media. The first model is a linear transport equation of Boltzmann type posed in the phase space (position and velocity). It accurately describes the physics but is very expensive to solve. The second model is a diffusion equation posed in the physical space. It is only valid in areas of high scattering, weak absorption, and smooth physical coefficients, but its numerical solution is...

A well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition

Sébastien Pernet (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The construction of a well-conditioned integral equation for iterative solution of scattering problems with a variable Leontovitch boundary condition is proposed. A suitable parametrix is obtained by using a new unknown and an approximation of the transparency condition. We prove the well-posedness of the equation for any wavenumber. Finally, some numerical comparisons with well-tried method prove the efficiency of the new formulation.