带源参数的热传导反问题的无网格方法

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.

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

In this paper, the finite point method is used to obtain the solution of a one-d imensional inverse heat conduction problem with a source parameter, and the corr esponding discrete equations are obtained. Compared with the numerical methods b ased 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 appr oximation functions. And the collocation method is used to discretize the govern ing partial differential equations. The finite point method has the advantages o f simpler numerical procedures, lower computation cost and arbitrary nodes. The result of a numerical example is presented to show the method is effective.