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Numerical Integration of Harmonic Functions with Restricted Sampling Data

Based on the idea of kriging and the radial basis function approximation, we develop in this paper a numerical scheme to integrate harmonic functions with restricted sampling data. To be more precise, the integration is performed by using the function values which are given as discrete sampling data on only part of the boundary. These problems often arise from non-destructive evaluation techniques in the engineering industry. The existence and uniqueness of the solution and the error estimation for the proposed numerical scheme are also discussed. Several numerical experimental results are presented for the verification on the accuracy and convergence of the method.