自然邻近无网格Petrov-Galerkin法 求解稳态热传导问题

自然邻近无网格Petrov-Galerkin法采用自然邻近插值构造试函数,并且在由Delaunay三角形构成的多边形局部子域上采用局部Petrov-Galerkin方法建立整体求解的平衡控制方程,是一种真正的无网格法。该方法能够方便准确地施加本质边界条件,而且得到的系统矩阵是带状稀疏矩阵。对该方法在稳态热传导问题中的应用进行了研究,算例结果表明该方法具有良好的数值精度和稳定性。

On Meshless Natural Neighbour Petrov-Galerkin Method for Stable Heat Conduction Problem

In meshless natural neighbour Petrov-Galerkin method,the natural neighbour interpolation is used as trial function and a weak form over the local polygonal sub-domains constructed by Delaunay triangulars is used to obtain the discretized system of equilibrium equations.It is a new truly meshless method because no background cells are needed for domain integration.The natural neighbour interpolants are strictly linear between adjacent nodes on the boundary of the convex hull,which facilitates the imposition of essential boundary conditions with ease as it is in the conventional finite element method.The system stiffness matrix in the present method is banded and sparse.The present method for solving stable heat conduction problem is presented and the numerical results show that the present method is quite accurate and stable.