Meshfree Computational Algorithms Based on Normalized Radial Basis Functions
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In this paper, new methods for solving mathematical modelling problems, based on the usage of normalized radial basis functions, are introduced. Meshfree computational algorithms for solving classical and inverse problems of mathematical physics are developed. The distinctive feature of these algorithms is the usage of moving functional basis, which allows us to adapt to solution particularities and to maintain high accuracy at relatively low computational cost. Specifics of neural network algorithms application to non-stationary problems of mathematical physics were indicated. The paper studies the matters of application of developed algorithms to identification problems. Analysis of solution results for representative problems of source components (and boundary conditions) identification in heat transfer equations illustrates that the elaborated algorithms obtain regularization qualities and allow us to maintain high accuracy in problems with considerable measurement errors.
KeywordsModelling Boundary value problem (BVP) Identification problem Meshfree method Artificial neural network (ANN) Normalized radial basis function (NRBF) Training Error functional Optimization
The work was supported by the Russian Foundation for Basic Research, project numbers 14-01-00660 and 14-01-00733.
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