# Coupling of transport and diffusion models in linear transport theory

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 36, Issue: 1, page 69-86
- ISSN: 0764-583X

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topBal, Guillaume, and Maday, Yvon. "Coupling of transport and diffusion models in linear transport theory." ESAIM: Mathematical Modelling and Numerical Analysis 36.1 (2010): 69-86. <http://eudml.org/doc/194097>.

@article{Bal2010,

abstract = {
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 than that of transport. We
are interested in the case when the domain is diffusive everywhere
except in some small areas, for instance non-scattering or
oscillatory inclusions. We present a natural coupling of the two
models that accounts for both the diffusive and non-diffusive
regions. The interface separating the models is chosen so that the
diffusive regime holds in its vicinity to avoid the calculation of
boundary or interface layers. The coupled problem is analyzed
theoretically and numerically. To simplify the presentation, the
transport equation is written in the even parity form. Applications
include, for instance, the treatment of clear or spatially
inhomogeneous regions in near-infra-red spectroscopy, which is
increasingly being used in medical imaging for monitoring certain
properties of human tissues.
},

author = {Bal, Guillaume, Maday, Yvon},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Linear transport; even parity formulation;
diffusion approximation; domain decomposition;
diffuse tomography.; Boltzmann equation; linear transport; diffusion approximation; diffuse tomography; diffusion equation},

language = {eng},

month = {3},

number = {1},

pages = {69-86},

publisher = {EDP Sciences},

title = {Coupling of transport and diffusion models in linear transport theory},

url = {http://eudml.org/doc/194097},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Bal, Guillaume

AU - Maday, Yvon

TI - Coupling of transport and diffusion models in linear transport theory

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 1

SP - 69

EP - 86

AB -
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 than that of transport. We
are interested in the case when the domain is diffusive everywhere
except in some small areas, for instance non-scattering or
oscillatory inclusions. We present a natural coupling of the two
models that accounts for both the diffusive and non-diffusive
regions. The interface separating the models is chosen so that the
diffusive regime holds in its vicinity to avoid the calculation of
boundary or interface layers. The coupled problem is analyzed
theoretically and numerically. To simplify the presentation, the
transport equation is written in the even parity form. Applications
include, for instance, the treatment of clear or spatially
inhomogeneous regions in near-infra-red spectroscopy, which is
increasingly being used in medical imaging for monitoring certain
properties of human tissues.

LA - eng

KW - Linear transport; even parity formulation;
diffusion approximation; domain decomposition;
diffuse tomography.; Boltzmann equation; linear transport; diffusion approximation; diffuse tomography; diffusion equation

UR - http://eudml.org/doc/194097

ER -

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