A novel domain decomposition method for highly oscillating partial differential equations

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...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2009-11, Vol.33 (11), p.1284-1288
Main Authors: Duan, Y., Tang, P.F., Huang, T.Z.
Format: Article
Language:English
Subjects:
Computational techniques
Domain decomposition
Exact sciences and technology
Kansa's method
Mathematical methods in physics
Mathematics
Meshless
Numerical analysis
Numerical analysis. Scientific computation
Oscillating PDE
Partial differential equations, boundary value problems
Physics
Radial basis function
Sciences and techniques of general use
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Summary: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.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2009.05.002