Numerical resolution of an anisotropic non-linear diffusion problem
Provides an efficient numerical method for solving anisotropic diffusion problems in computational physics, but the approach is incremental as it extends existing Asymptotic-Preserving techniques to a specific class of problems.
The paper develops an Asymptotic-Preserving scheme for an anisotropic non-linear diffusion problem with a small parameter, achieving accuracy and computational cost independent of the anisotropy strength.
This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \varepsilon, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable vector function b. The equation being supplemented with Neumann boundary conditions, the limit \varepsilon \infty 0 is demonstrated to be a singular perturbation of the original diffusion equation. To address efficiently this problem, an Asymptotic-Preserving scheme is derived. This numerical method does not require the use of coordinates adapted to the anisotropy direction and exhibits an accuracy as well as a computational cost independent of the anisotropy strength.