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带源参数的二维热传导反问题的无网格方法
引用本文:程荣军,程玉民.带源参数的二维热传导反问题的无网格方法[J].力学学报,2007,39(6):843-847.
作者姓名:程荣军  程玉民
作者单位:上海大学上海市应用数学和力学所,200072 上海大学上海市应用数学和力学所,200072
基金项目:国家自然科学基金,上海市重点学科建设项目
摘    要:利用无网格有限点法求解带源参数的二维热传导反问题,推导了相应的离散方程. 与 其它基于网格的方法相比,有限点法采用移动最小二乘法构造形函数,只需要节点信息,不 需要划分网格,用配点法离散控制方程,可以直接施加边界条件,不需要在区域内部求积分. 用有限点法求解二维热传导反问题具有数值实现简单、计算量小、可以任意布置节点等优点. 最后通过算例验证了该方法的有效性.

关 键 词:无网格方法  有限点法  移动最小二乘法  热传导反问题  源参数
文章编号:0459-1879(2007)06-0843-05
收稿时间:2007-02-05
修稿时间:2007-02-05

THE MESHLESS METHOD FOR A TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM WITH A SOURCE PARAMETER
Cheng Rongjun,Cheng Yumin.THE MESHLESS METHOD FOR A TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM WITH A SOURCE PARAMETER[J].chinese journal of theoretical and applied mechanics,2007,39(6):843-847.
Authors:Cheng Rongjun  Cheng Yumin
Abstract:Inverse problems are difficult to be solved in scientific research. And they are widely applied in the aerospace, nuclear physics, metallurgy and other fields. The finite difference method and the finite element method are main numerical methods to obtain numerical solutions of inverse problems. The finite point method is one of meshless methods. Comparing with the numerical methods based on mesh, such as finite element method and boundary element method, the finite point method only needs the scattered nodes instead of meshing the domain of the problem when the shape function are formed. For problems with complicated domain which need to be re-meshed, the finite point method has the advantage of that no mesh is needed. In this paper, the finite point method is used to obtain numerical solutions of two-dimensional inverse heat conduction problems with a source parameter, and the corresponding discretized equations are obtained. The collocation method is used to discretize the governing partial differential equations, and boundary conditions can be directly enforced without numerical integration in the problem domain. This reduces the computation cost greatly. A numerical example is presented to show the method in this paper is effective. The finite point method, which is for two-dimensional inverse heat conduction problems with a source parameter, presented in this paper has some advantages of arbitrary nodes distribution, simple numerical procedures and low computation cost. The researches in this paper provide a new numerical method for inverse heat conduct problems, and can be applied to other inverse problems.
Keywords:meshless method  the finite point method  the moving least-square approximation  inverse heat conduction problem  source parameter  
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