2003
DOI: 10.1051/m2an:2003059
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: 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 … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

2
58
0
1

Year Published

2008
2008
2018
2018

Publication Types

Select...
4
4

Relationship

1
7

Authors

Journals

citations
Cited by 45 publications
(61 citation statements)
references
References 24 publications
2
58
0
1
Order By: Relevance
“…It can be also incorporated in a domain decomposition method to deal with space varying mean free path, in the spirit of [23,49].…”
Section: Remark 3 (Spatial Derivatives Discretization)mentioning
confidence: 99%
“…It can be also incorporated in a domain decomposition method to deal with space varying mean free path, in the spirit of [23,49].…”
Section: Remark 3 (Spatial Derivatives Discretization)mentioning
confidence: 99%
“…Then using (18) and relation (3) give ρ * = ρ (0) hence g (0) F = 0. Consequently, the last equation (16) of our system can be eliminated.…”
Section: Splitting Of the Perturbative Non-equilibrium Effects By Usimentioning
confidence: 99%
“…When the system stays near equilibrium, the problem can be reduced using a macroscopic description, only depending on t and x. Several strategies can be used to solved multiscale problems (see for example [9], [8], [11] or [2]), among them, the micro-macro decomposition introduced in [1] leads to a coupling of two equations: a macroscopic one for the mean part of f (in velocity) and a microscopic one for the remainder part (called perturbation).…”
Section: Introductionmentioning
confidence: 99%