A hybrid method for anisotropic elliptic problems based on the coupling of an Asymptotic-Preserving method with the Asymptotic-Limit model
This work addresses the computational efficiency of solving anisotropic elliptic problems for researchers in numerical analysis and computational physics, but the improvement is incremental as it combines existing techniques.
The authors propose a hybrid method coupling an Asymptotic-Preserving model with its asymptotic limit model to efficiently solve highly anisotropic elliptic problems, reducing computational time in regions where the anisotropy parameter is small.
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.