Generalized Fokker-Planck theory for electron and photon transport in biological tissues: application to radiotherapy.
Olbrant, Edgar, Frank, Martin (2010)
Computational & Mathematical Methods in Medicine
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Olbrant, Edgar, Frank, Martin (2010)
Computational & Mathematical Methods in Medicine
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Martin Šolc (1981)
Acta Universitatis Carolinae. Mathematica et Physica
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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...
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...
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.