A novel domain decomposition method for highly oscillating partial differential equations

摘要

This paper is devoted to designing a novel domain decomposition method (DDM) for highly oscillating partial differential equations (PDE), especially, where the asymmetric meshless collocation method using radial basis functions (RBF), also Kansa's method is applied for a numerical solutions. It is found that the numerical error become worse when the original solution become more oscillating. To conquer this defect, we use a novel domain decomposition method which is motivated by time parallel algorithm. This DDM is based on a decomposition of computational domain by a coarse centers and a finer distribution of distinct centers. A corrector is designed to obtain better numerical solution after several iteration. Theoretical analysis and numerical examples are given to demonstrate the accuracy and efficiency of the proposed algorithm.