用边界元法求解Signorini问题的线性互补法

对Poisson方程的Signorini问题,提出了利用边界积分方程的线性互补解法。用Green公式和Laplace方程的基本解推导得该问题的边界积分方程,利用边界位势及其法向导数的Signorini约束,由该离散化积分方程导出一个形如U1≥0,AIIU1+N≥0且U1T(AU1+N)=0的标准线性互补问题,且Signorini边界约束仅作用于边界位势。再用投影超松弛迭代法求解线性互补问题,数值结果表明该方法是有效的。

The Linear Complementarity Method for the Signorini Problem Using Boundary Element Method

The boundary element-linear complementarities method for solving the Poisson Signorini problem is presented in this paper.Both Green’s formula and the fundamental solution of the Laplace equation have been used to solve the boundary integral equation.By imposing the Signorini constraints of the potential and its normal derivative on the boundary,the discrete integral equation can be written into a standard linear complementarities problem in the form of U1≥0,AIIU1+N≥0 and UT1(AU1+N)=0,which is affected by the Signorini boundary constraints with the boundary potential variable only.A projected successive over-relaxation iterative method is employed to solve the problem,and numerical results are presented to illustrate the efficiency of this method.