The Research And Application Of Improved Meshless Method And DB Wavelet Meshless Method

The paper studied meshless local radial point interpolation method for the helmholtz equation and daubechies wavelet meshless method of numerical calculation in the electromagnetic field.Firstly, a radial basis function coupled with a polynomial basis function as a trail function in the meshless local radial point interpolation method (LRPIM). Paper describes shape function of properties in RPIM. The shape function was obtained in trail function has the Kronecker Delta property, and no additional treatment was required to impose essential boundary conditions. Compared with element-free Galerkin method, the presented method was one of the "truly meshless" methods since it did not require any background integration cells. The algorithm of meshless LRPIM is introduced to helmholtz equation, the discrete equation was established by the meshless local Petrov-Galerkin method, and specific numerical integration method was given. The numerical results showed that the meshless LRPIM for the helmholtz equation had a number of advantages, such as conciseness, efficacious, quite good accuracy.Then, wavelet functions are applied to element-free Galerkin method, based on wavelet function compactly supported and orthogonal. Combining with wavelet functions and advantages of meshless method, established the wavelet function meshless method. It can overcome other field function in the calculation of redundancy, reduce computation cost or improve the calculation accuracy characteristics. The thesis on several commonly used wavelet function is expounded, corresponding formula of the wavelet function meshless method is deduced, and the wavelet function meshless method is applicated to electromagnetic field in the issue, the discrete model are described. Finally the calculation results proved that the wavelet function meshless method is stabilized.Lastly, the combination of DB wavelet and meshless galerkin method solve electromagnetic field problems. The scaling function of DB wavelet can be directly used to approximate unknown field function instead of trying to structure shape function. Through the meshless galerkin method, produce discrete model of DB wavelet meshless method for Poisson equation. Due to the lack of Kroneker delta properties in scaling functions, using penalty function method to dispose imposition of boundary conditions. Numerical example proved effectiveness and high precision of this method.