Interpolation Method of Radial Basis Function for Partial Differential Equations and Calculation of Seepage Problem

Abstract: Radial basis function interpolation in the past dozen years to develop a numerical solution of differential equations of the meshless method, the method of differential equations without numerical grid dispersion, thus avoiding not only the mesh generation complex process, but also can significantly reduce the traditional grid method (such as the finite element method, finite difference method), such as mesh distortion due to the adverse impact.This article summarizes the radial basis function interpolation method for one-dimensional, two-dimensional interpolation function fitting, and radial basis function solution before mooring and equations, this method has been applied to simple flow problems, have been relatively satisfied with the results.The full text is divided into five chapters. The first chapter is the introduction, introduces the meshless radial basis function method and the development and research in recent years, the status quo. Chapter II is to prepare the knowledge, first introduced the radial basis function interpolation of the basic theory and methods, and then introduced a special kind of radial basis function MQ function and radial basis function interpolation of the numerical solution of partial differential equations theory and methods. Chapter III of this method is applied to one-dimensional, two-dimensional interpolation of the classic examples and calculation examples of partial differential equations; from the results of numerical experiments we can see that the radial basis function interpolation in the ease of use and accuracy than the traditional grid method has been greatly improved. Chapter IV of the mathematical model for the flow and boundary conditions. This paper describes the basic equation of flow movement and the basic equation of initial conditions and boundary conditions, and for each specific flow model of a given initial conditions and boundary conditions. Finally, the radial basis function interpolation applied a simple two-dimensional seepage problem.Finally, conclusions and outlook…
Key words: Meshless method ; radial basis function ; Interpolation method ; Seepage problems

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