基于微观-宏观分解的高各向异性椭圆方程渐近保持方法
An Asymptotic-Preserving method for highly anisotropic elliptic equations based on a micro-macro decomposition
AI总结：
提出一种基于微观-宏观分解的渐近保持格式，用于高效求解高各向异性扩散方程，具有对各向异性参数的一致收敛性、适用于非均匀非对齐各向异性场，并能简单推广到非恒定各向异性强度情形。
摘要：
本文关注的是引入一种非常高效的渐近保持格式，用于求解高各向异性扩散方程。该格式的特征包括：对各向异性参数 $0<\eps <<1$ 的一致收敛性，适用于（在笛卡尔网格上）非均匀和非对齐的各向异性场 $b$，并能简单推广到非恒定各向异性强度 $1/\eps$ 的情形。数学方法和数值方案与之前的工作 [Degond et al. (2010), arXiv:1008.3405v1] 不同，并指出了其显著优势。
英文摘要：
The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with respect to the anisotropy parameter $0<\eps <<1$, the applicability (on cartesian grids) to cases of non-uniform and non-aligned anisotropy fields $b$ and the simple extension to the case of a non-constant anisotropy intensity $1/\eps$. The mathematical approach and the numerical scheme are different from those presented in the previous work [Degond et al. (2010), arXiv:1008.3405v1] and its considerable advantages are pointed out.
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