泊松问题的无网格解法

利用线性系统的叠加原理提出了一种基于虚边界配点的无网格解法用于位势问题的数值计算.该算法通过把求解函数分为齐次解和特解2部分,对特解采用局部径向基函数近似,对齐次解采用虚边界配点的方法处理.采用虚边界配点,不需要边界单元积分,避免了普通边界元解法中边界奇异积分的复杂计算,也不需要额外的方程来计算域内物理量.最后通过具体的算例检验了所提算法的有效性和可行性,数值结果和解析解取得了较好的吻合.

A Meshless Method for Poisson Problems

A boundary-type meshless method is presented, which couples virtual boundary collocation method and the radial basis functions approximation to analyze Poisson problems. The particular solution is approximated by using radial basis functions, and the corresponding homogeneous solution is solved by means of the virtual boundary collocation method. As a result, a new method fully independent of mesh is developed. In this method, only some points are needed, so it avoids the computation of element integral on the boundary and doesn't need extra equations to compute internal parameters in the domain. Finally, a numerical experiment is implemented to verify the efficiency of this method and numerical results are in good agreement with the exact ones.