Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case

Degond, Pierre; Deluzet, Fabrice; Maldarella, Dario; Narski, Jacek; Negulescu, Claudia; Parisot, Martin

doi:10.1051/proc/2011010

Cited by 2 publications

(2 citation statements)

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“…In contrast, for Problem (44)(45)(46)(47)(48) the non zeros elements remain 2.3 times larger that of Problem (40) whatever the mesh size. The efficiency is further improved by implementing a hybrid method coupling the AP reformulation (44)(45)(46)(47)(48) and the limit problem in the region where the asymptotic parameter is small [50,37]. Indeed this last model furnishes a solution that does not depend on the z coordinate, the discretization of this model gives rise to a smaller system matrix.…”

Section: Duality Based Reformulationmentioning

confidence: 99%

Asymptotic-Preserving methods and multiscale models for plasma physics

Degond

Deluzet

2017

Journal of Computational Physics

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The purpose of the present paper is to provide an overview of As ymptotic- Preserving methods for multiscale plasma simulations by ad dressing three sin- gular perturbation problems. First, the quasi-neutral lim it of fluid and kinetic models is investigated in the framework of non magnetized as well as magne- tized plasmas. Second, the drift limit for fluid description s of thermal plasmas under large magnetic fields is addressed. Finally efficient nu merical resolutions of anisotropic elliptic or diffusion equations arising in ma gnetized plasma simu- lation are reviewed

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Section: Duality Based Reformulationmentioning

confidence: 99%

Asymptotic-Preserving methods and multiscale models for plasma physics

Degond

Deluzet

2017

Journal of Computational Physics

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“…These considerations lead us to the introduction of a domain decomposition strategy, where the AP-model is used where ε (z) is of order one, and the L-model in the regions where ε (z) is "small" enough, both models being coupled with appropriate interface conditions. Such a coupling is studied in the one-dimensional framework in [6]. We propose here to extend this coupling strategy to 2D problems and to provide the first analysis results.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Method for Anisotropic Elliptic Problems Based on the Coupling of an Asymptotic-Preserving Method with the Asymptotic Limit Model

Crestetto¹,

Deluzet²,

Negulescu³

2016

SIAM J. Sci. Comput.

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This paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems. The anisotropy is aligned with one coordinate axis and its strength is described by a parameter ε ∈ (0, 1], which can largely vary in the study domain. Our hybrid model is based on asymptotic techniques and couples (spatially) an asymptotic-preserving model with its asymptotic limit model, the latter being used in regions where the anisotropy parameter ε is small. Adequate coupling conditions link the two models. The aim of this hybrid procedure is to reduce the computational time for problems where the region of small ε-values extends over a significant part of the domain, and this is due to the reduced complexity of the limit model. Introduction.The present work is a contribution to the numerical resolution of highly anisotropic elliptic equations, the anisotropy being aligned with one coordinate axis and described by a perturbation parameter ε ∈ (0, 1], varying considerably in the study domain. The approach presented here is based on a coupling strategy, solving an asymptotic-preserving (AP) reformulation of the elliptic problem, where ε is nonnegligible, and solving the corresponding asymptotic limit model, where ε is quasi-vanishing. The strategy we propose is particularly well suited for physical systems in which the anisotropy parameter ε is very small in a large part of the study domain.Such types of directionally anisotropic diffusion systems are common in physical applications, such as plasma physics [4,13,14,16,25,26].The application which was at the origin of the present work comes from strongly magnetized ionospheric plasmas [1,15,21]. The problem we shall study here is extracted from the dynamo model and represents an elliptic equation for the computation of the electric potential in two-dimensions, i.e.,

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Hybrid model for the Coupling of an Asymptotic Preserving scheme with the Asymptotic Limit model: The One Dimensional Case

Cited by 2 publications

References 5 publications

Asymptotic-Preserving methods and multiscale models for plasma physics

Asymptotic-Preserving methods and multiscale models for plasma physics

A Hybrid Method for Anisotropic Elliptic Problems Based on the Coupling of an Asymptotic-Preserving Method with the Asymptotic Limit Model

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