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.
Inverse problems are widely found 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 for inverse problems.The finite point method is a meshless method.Comparing with the numerical methods based on mesh,such as finite element method and boundary element method,the finite point method only uses scattered nodes without having to mesh the domain of the problem when the shape function is formed. 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 given to show the effectiveness of the method.The finite point method can also be applied to other inverse problems.
出处
《力学学报》
EI
CSCD
北大核心
2007年第6期843-847,共5页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金(10571118)
上海市重点学科建设(Y0103)资助项目.~~
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
meshless method
the finite point method
the moving least-square approximation
inverse heat conduction problem
source parameter
