The Research And Application Of Improved Element-free Galerkin Method In The Temperature

The purpose of this paper is to develop an improved element-free Galerkin (IEFG)method, using it to temperature field problems. However, this method needs to be furtherstudied in heat transfer problems. This paper successfully applies it in heat transferproblems, the works presented in the thesis are as follows:Firstly, it is given that the influence of different weight functions and different basisfunctions on one-dimensional shape functions and their derivative of MLSM and theimpact of the MLSM on the estimate value.Then, this paper presents an improved moving least-square (IMLS) approximationin which the orthogonal function system with a weight function is used as the basisfunction. By combining the element-free Galerkin (EFG) method and the IMLSapproximation, IEFG method is derived. Lagrange multiplier method and penaltyfunction method are used to deal with essential boundary conditions. IEFG method isapplied in one-dimension, two-dimensional rectangular domain, two-dimensional circulardomain and three-dimension typically stable heat transfer problems. The results will becompared with exact solutions, which prove that the method is effective to solve thestable heat transfer problems.Lastly, by combining the stochastic element-free Galerkin (SEFG) method and theIMLS method, a Taylor expansion improved stochastic element-free Galerkin method,Neumann expansion improved Monte-Carlo stochastic element-free Galerkin method andperturbation expansion improved stochastic element-free Galerkin methods are derived.These methods are applied in stochastic heat transfer problems. The results will becompared with the exact solutions or pseudo excitation method solutions, which provethat the method is a simple, effective and high accuracy method.