# A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem

François Golse; Shi Jin; C. David Levermore

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 37, Issue: 6, page 869-892
- ISSN: 0764-583X

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topGolse, François, Jin, Shi, and David Levermore, C.. "A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem." ESAIM: Mathematical Modelling and Numerical Analysis 37.6 (2010): 869-892. <http://eudml.org/doc/194196>.

@article{Golse2010,

abstract = {
We present a domain decomposition theory on an interface problem
for the linear transport equation between a diffusive and a non-diffusive region.
To leading order, i.e. up to an error of the order of the mean free path in the
diffusive region, the solution in the non-diffusive region is independent of the
density in the diffusive region. However, the diffusive and the non-diffusive regions
are coupled at the interface at the next order of approximation. In particular, our
algorithm avoids iterating the diffusion and transport solutions as is done in most
other methods — see for example Bal–Maday (2002). Our analysis is based instead on an accurate description of the boundary
layer at the interface matching the phase-space density of particles leaving the
non-diffusive region to the bulk density that solves the diffusion equation.
},

author = {Golse, François, Jin, Shi, David Levermore, C.},

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

keywords = {Domain decomposition; transport equation; diffusion approximation; kinetic-fluid coupling.; domain decomposition; kinetic-fluid coupling; interface problem; linear transport equation; algorithm; boundary layer},

language = {eng},

month = {3},

number = {6},

pages = {869-892},

publisher = {EDP Sciences},

title = {A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem},

url = {http://eudml.org/doc/194196},

volume = {37},

year = {2010},

}

TY - JOUR

AU - Golse, François

AU - Jin, Shi

AU - David Levermore, C.

TI - A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 37

IS - 6

SP - 869

EP - 892

AB -
We present a domain decomposition theory on an interface problem
for the linear transport equation between a diffusive and a non-diffusive region.
To leading order, i.e. up to an error of the order of the mean free path in the
diffusive region, the solution in the non-diffusive region is independent of the
density in the diffusive region. However, the diffusive and the non-diffusive regions
are coupled at the interface at the next order of approximation. In particular, our
algorithm avoids iterating the diffusion and transport solutions as is done in most
other methods — see for example Bal–Maday (2002). Our analysis is based instead on an accurate description of the boundary
layer at the interface matching the phase-space density of particles leaving the
non-diffusive region to the bulk density that solves the diffusion equation.

LA - eng

KW - Domain decomposition; transport equation; diffusion approximation; kinetic-fluid coupling.; domain decomposition; kinetic-fluid coupling; interface problem; linear transport equation; algorithm; boundary layer

UR - http://eudml.org/doc/194196

ER -

## References

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