A meshless algorithm with moving least square approximations for elliptic Signorini problems

Abstract

Based on the moving least square (MLS) approximations and the boundary integral equations (BIEs), a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm.

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

“…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.…”

“…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].…”

“…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.…”

“…Furthermore, although the BNM requires no mesh, the method in Ref. [21] requires twice the number of unknowns and system equations. These procedures increase the computational complexity and thus influence the computing efficiency and limit the applicability.…”