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

This paper presents a hybrid numerical method to solve efficiently a class of highly anisotropic elliptic problems. The anisotropy is aligned with one coordinateaxis 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. Aim of this hybrid procedure is to reduce the computational time for problems where the region of small εvalues extends over a significant part of the domain, and this due to the reduced complexity of the limit model.