Signorini问题的无网格投影迭代法

Signorini问题是一类重要的数学物理问题,该问题的Signorini互补条件位于边界上,特别适合用边界型方法求解.利用投影算子,首先将Signorini边界条件转化为不动点方程,得到Signorini问题的迭代格式,然后用无网格边界点方法求解.此种算法的优点在于只须在原有的无网格边界点程序中做少量的改进,且迭代效率高,计算误差小.数值结果表明,该算法较边界元方法更有效.

On a Meshless Projection Iterative Method for Signorini Problems

Signorini problem is an important partial differential boundary value problem .Since the Signorini complementary conditions lie on the boundary of the region ,it is suitable for boundary type method .Ac-cording to a projection operator ,the Signorini boundary conditions have been transformed into a fixed point equation .T hen ,projection iterative scheme of Signorini problem based on the fixed point equation has been established .The meshless boundary node method (BNM ) is introduced for solving Signorini problem in the iterative scheme .T he presented algorithm is easy to be implied .It only needs the minimal change of the BNM programming .The numerical results show that the algorithm is more effective than the boundary element method .