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arXiv · 1511.00917

A hybrid method for anisotropic elliptic problems based on the coupling of an Asymptotic-Preserving method with the Asymptotic-Limit model

Anais Crestetto·Fabrice Deluzet·Claudia Negulescu
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Abstract

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 $\eps \in (0,1]$, 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 $\eps$ is small. Adequate coupling conditions link the two models. Aim of this hybrid procedure is to reduce the computational time for problems where the region of small $\eps$-values extends over a significant part of the domain, and this due to the reduced complexity of the limit model.

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Anais Crestetto, Fabrice Deluzet, Claudia Negulescu. 2015-11-03. A hybrid method for anisotropic elliptic problems based on the coupling of an Asymptotic-Preserving method with the Asymptotic-Limit model. https://arxiv.org/abs/1511.00917

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