Reproducing kernel particle method and its modification

Some Studies of the Reproducing Kernel Particle Method

Abstract. Interests in meshfree (or meshless) methods have grown rapidly in the recent years in solving boundary value problems arising in mechanics, especially in dealing with difficult problems involving large deformation, moving discontinuities, etc. Rigorous error estimates of a meshfree method, the reproducing kernel particle method (RKPM), have been theoretically derived and experimentall...

Method of Reproducing Kernel

Multiresolution Reproducing Kernel Particle Methods in Acoustics

In the analysis of complex phenomena of acoustic systems, the computational model-ing requires special attention for a realistic representation of the physics. As a powerful tool, the nite element method has been widely used in the study of complex systems. In order to capture the important physical phenomena, p-nite elements and/or hp-nite elements are employed. The reproducing kernel particle...

Moving Least Square Reproducing Kernel Method ( III ) : Wavelet Packet & Its

This work is a natural extension of the work done in Part II of this series. A new partition of unity | the synchronized reproducing kernel (SRK) interpolant|is proposed within the framework of moving least square reproducing kernel representation. It is a further development and generalization of the reproducing kernel particle method (RKPM), which demonstrates some superior computational capa...

Reproducing Kernel Space Hilbert Method for Solving Generalized Burgers Equation

In this paper, we present a new method for solving Reproducing Kernel Space (RKS) theory, and iterative algorithm for solving Generalized Burgers Equation (GBE) is presented. The analytical solution is shown in a series in a RKS, and the approximate solution u(x,t) is constructed by truncating the series. The convergence of u(x,t) to the analytical solution is also proved.