Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem
Efficient discretization and preconditioning of the singularly perturbed reaction-diffusion problem
复制标题
奇扰动反应扩散问题的高效离散化和预处理
DOI：
10.1016/j.camwa.2022.01.031
复制
发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Jacob Jacavage
中科院分区：
文献类型：
--
作者：
Constantin Bacuta;Daniel Hayes;Jacob Jacavage
我们考虑反应扩散问题，并提出有效的方法来离散和预处理的奇异摄动的情况下，反应项占主导地位的方程。利用最佳测试范数和鞍点重构的概念，我们提供了有效的离散过程均匀和非均匀网格。我们提出了一个预处理策略，适用于大范围的扰动参数。数值例子来说明该方法的效率包括一个问题上的单位平方。
We consider the reaction diffusion problem and present efficient ways to discretize and precondition in the singular perturbed case when the reaction term dominates the equation. Using the concepts of optimal test norm and saddle point reformulation, we provide efficient discretization processes for uniform and non-uniform meshes. We present a preconditioning strategy that works for a large range of the perturbation parameter. Numerical examples to illustrate the efficiency of the method are included for a problem on the unit square.