基本解法求解Signorini问题

On Method of Fundamental Solutions for Signorini Problem

将基本解法与投影迭代算法相结合求解Signorini问题,引入投影迭代算子将边界不等式约束转化为不动点方程,并采用一种新的投影迭代格式.在迭代过程中,采用基本解法只需要构造一次系数矩阵,从而使得数值计算变得简单且有效.最后,算例的数值结果表明了基本解方法比边界元方法收敛速度快,耗费时间少,精度更高.

The method of fundamental solutions and the iterative projection algorithm have been combined for the solution of the Signorini problem. Introducing a projection iterative operator, inequality bounding constraints are transformed into a fixed point equation, and a new iteration scheme is developed in the iterative process. With the method of fundamental solutions, the system matrix only has to be computed once. Thus, the numerical calculation becomes simple and effective. Finally, the numerical results show that the method of fundamental solutions is faster than the boundary element method, and it has a little time consumption and higher accuracy.