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Abstract
Based on the coupling of the natural boundary integral method and the finite elements method, we mainly investigate the numerical solution of Neumann problem of harmonic equation in an exterior elliptic. Using our trigonometric wavelets and Galerkin method, there obtained stiffness matrix is symmetrical and circulant, which lead us to a fast numerical method based on fast Fourier transform. Furthermore, we do not need to compute the entries of the stiffness matrix. On the other hand, we prove that the numerical solution possesses exponential convergence rate. Especially, examples state that our method still has good accuracy for small j when the solution u 0(θ) is almost singular.
Acknowledgements
The author presents his sincere thanks to professor Lin Wei for his valuable and helpful comments and suggestions. This work has been Supported by Scientific Research Fund of Hunan Provincial Education Department (No. 07C335 and No. 07A025A), Nature Science Foundation of Hunan Province and the Construct Program of the Key Discipline in Hunan Province.