带源参数的热传导反问题的无网格方法

The meshless method for solving the inverse heat conduction problem with a source parameter

利用无网格有限点法求带有源参数的一维热传导反问题,推导了相应的离散方程.与其他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,用配点法离散求解方程,可以直接施加边界条件,不需要在区域内部求积分,减小了计算量.用有限点法求解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.

In this paper, the finite point method is used to obtain the solution of a one-dimensional inverse heat conduction problem with a source parameter, and the corresponding discrete equations are obtained. Compared with the numerical methods based on mesh, the finite point method only needs the scattered nodes instead of meshing the domain of the problem. The finite point method is a meshless method in which the moving least-square approximation is used to form the meshless approximation functions. And the collocation method is used to discretize the governing partial differential equations. The finite point method has the advantages of simpler numerical procedures, lower computation cost and arbitrary nodes. The result of a numerical example is presented to show the method is effective