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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

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 much cheaper...

Coupling of transport and diffusion models in linear transport theory

Guillaume Bal, Yvon Maday (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Curve reconstruction from a set of measured points

Hlavová, Marta (2021)

Programs and Algorithms of Numerical Mathematics

In this article, a method of cubic spline curve fitting to a set of points passing at a prescribed distance from input points obtained by measurement on a coordinate measuring machine is described. When reconstructing the shape of measured object from the points obtained by real measurements, it is always necessary to consider measurement uncertainty (tenths to tens of micrometres). This uncertainty is not zero, therefore interpolation methods, where the resulting curve passes through the given...

Curved triangular finite C m -elements

Alexander Ženíšek (1978)

Aplikace matematiky

Curved triangular C m -elements which can be pieced together with the generalized Bell’s C m -elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order 2 ( m + 1 ) in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the...

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