Computational method for a singular perturbation problem via domain decomposition and its parallel implementation

摘要

In this paper, a computation method for the nonlinear problem with a small perturbation parameter via domain decomposition is presented. We apply a combination of the two approaches to solving the problem: iterative algorithms for domain decomposition and a grid refinement technique on subdomains. Two iterative algorithms are examined: the first one is the Schwarz alternating procedure and the second algorithm is highly suitable for parallel computing. Numerical examples are provided.