A complex variable meshless local Petrov-Galerkin method for transient heat conduction problems  

作　　者：王启防 戴保东 栗振锋 

机构地区：[1]Department of Engineering Mechanics, Taiyuan University of Science & Technology [2]College of Transportation & Logistics, Taiyuan University of Science & Technology

出　　处：《Chinese Physics B》2013年第8期238-244,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.51078250);the Research Project by Shanxi Scholarship Council of Shanxi Province,China(Grant No.2013-096);the Scientific&Technological Innovation Program for Postgraduates of Taiyuan University of Science and Technology,China(Grant No.20125026)

摘　　要：On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.

关 键 词：meshless method complex variable moving least-square method complex variable meshless localPetrov-Galerkin method transient heat conduction problems 

分 类 号：O157.5[理学—数学] O551.3[理学—基础数学]