基于径向基函数的自适应网格方法

本文给出了一种基于径向基函数的自适应网格方法．该方法利用网格依赖方法的解与径向基函数插值解的信息来细化或粗化网格，充分利用了径向基函数计算格式简单、节点配置灵活的优点与网格依赖方法的稳健性．提出的算法很容易编程实现．数值算例表明该算法可以在解变化剧烈的区域加密网格，在解变化平缓的地方粗化网格，从而在保证相同数值求解精度的情况下，能够极大地节省计算量．

An Adaptive Mesh Method Based on Radial Basis Function

In this paper, we propose an adaptive mesh method based on the radial basis function. The proposed method uses the information of the numerical solution provided by the mesh dependence method and the difference solution from the radial basis function to refine or coarse the mesh. Our method takes full advantage of the simple format and the flexible node configuration that the radial basis function possessed and the robustness of the mesh-depended method. The proposed algorithm is easy to implement. The numerical examples show that the proposed algorithm can refine the mesh in the region where the solution changes dramatically and coarsen the mesh in the region where the solution changes gradually. Therefore, it can save an enormous amount of calculating time while ensuring the same numerical accuracy.