A robust overlapping Schwarz domain decomposition algorithm for time-dependent singularly perturbed reaction-diffusion problems
详细信息 查看全文
- 作者：Sunil Kumar ; S. Ch ; ra Sekhara Rao
- 关键词：Singular perturbation ; Parabolic reaction&ndash ; diffusion problems ; Parameter-robust ; Domain decomposition ; Coupled system
- 刊名：Journal of Computational and Applied Mathematics
- 出版年：1 May, 2014
- 年：2014
- 卷：261
- 期：Complete
- 页码：127-138
- 全文大小：436 K
文摘
In this work, we consider a singularly perturbed parabolic problem of reaction-diffusion type. To solve this problem numerically we develop an overlapping Schwarz domain decomposition method, where we use the asymptotic behaviour of the exact solution for domain partitioning. We prove that the method gives uniform numerical approximations of first order in time and almost second order in space. Furthermore, we address the much faster convergence of the algorithm for small perturbation parameter . To be more specific, we prove that, when is small, just one iteration is required to achieve the desired accuracy. We then extend the method to a system of singularly perturbed parabolic problems of reaction-diffusion type. Numerical experiments support the theoretical results and demonstrate the effectiveness of the method.