Study On The Weight Function In The Dimension Splitting Element Free Galerkin Method For Linear Partial Differential Equations

Dimension splitting element free Galerkin method,as one of the meshless methods rising in recent years,improves the computational efficiency and accuracy compared with the improved element free Galerkin method in solving three-dimensional problems.In this method,the three-dimensional problem is first divided into a series of two-dimensional problems and one-dimensional problems,then the improved element free Galerkin method is used for two-dimensional problems,and the finite difference method is used for one-dimensional problems.As the key of the method,the weight function has a great influence on the calculation results.In this paper,the weight function is studied,and four different weight functions are selected for comparative study;Secondly,aiming at the three-dimensional transient heat conduction problem and three-dimensional wave equation,the numerical examples are classified according to the different boundary conditions,and the MATLAB calculation program of relevant examples is compiled.The influence of node distribution,influence domain factor d_max and time step on the calculation accuracy and efficiency is analyzed when the form of weight function and the parameters in weight function are different.The results show that the exponential function is used as the weight function,and ? should be 0.35 or 0.4 in solving the problems with essential boundary conditions by using the dimension splitting element free Galerkin method,which can obtain better calculation accuracy and efficiency;When solving the problems with natural boundary conditions,the quartic spline function should be taken as the weight function;When solving the problem with mixed boundary conditions,the positive definite compactly supported radial basis function should be taken as the weight function.