A HYBRID METHOD FOR ANISOTROPIC ELLIPTIC PROBLEMS BASED ON THE COUPLING OF AN ASYMPTOTIC-PRESERVINGMETHOD 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 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.