A projection iterative algorithm boundary element method for the Signorini problem

Abstract

We propose a projection iterative algorithm based on a fixed point equation for solving a certain class of Signorini problem. The satisfaction of the Signorini boundary conditions is verified in a projection iterative manner, and at each iterative step, an elliptic mixed boundary value problem is solved by a boundary element method which is suitable for any domain. We prove the convergence of the algorithm by the property of projection. The advantage of this algorithm is that it is easy to be implemented and converge quickly. Some numerical results show the accuracy and effectiveness of the algorithm.

Meshless projection iterative analysis of Signorini problems using a boundary element-free method

“…Consequently, the issues encountered in Refs. [20][21][22] are successfully overcome. Besides, compared with the method used in Refs.…”

“…Besides, the solution of Signorini problems is further complicated by the fact that the number and the position of the points where the change from one type of boundary condition to the other occurs are unknown [13,14]. However, because such conditions only occur on the boundary of the domain, boundary-type numerical methods such as the boundary element method (BEM) are particularly suitable for the solution of Signorini problems [2,6,[13][14][15][16][17][18][19][20][21][22]. The BEM reduces the computational dimensions of the original problem by one, but still involves boundary meshing.…”

“…An implicit projection iterative scheme has been developed and applied with the BEM [20] and the BNM [21] leading to accurate results. However, the implicit scheme converts Signorini boundary conditions into a sequence of Robin boundary conditions.…”

“…Moreover, the coefficient matrices of the discrete system equations in Refs. [20,21] have to be recomputed at each iteration. Furthermore, although the BNM requires no mesh, the method in Ref.…”

“…Among them are a decomposition-coordination scheme [13], an optimization scheme [6,[14][15][16], a switching scheme [17] and a linear complementary scheme [18]. Recently, the projection iterative scheme has become a popular technique for handling Signorini conditions [7][8][9][10][20][21][22].…”