The method of fundamental solutions for solving direct and inverse Signorini problems

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

“…It can be found that the results of our BEFM match those of given in Refs. [3,14,15,18,19,21,22]. Figs.…”

“…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.…”

“…Other than the BEM, the only other method which has been used extensively for the solution of Signorini problems of various types is the method of fundamental solutions (MFS) [14][15][16]. Some regularization techniques have been proposed to investigate the stability and accuracy of the MFS [38].…”

“…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].…”

Fast-multipole accelerated singular boundary method for large-scale three-dimensional potential problems

“…The method belongs to the family of meshless boundary collocation methods [3][4][5][6][7][8][9][10] and can be viewed as one kind of modified method of fundamental solutions (MFS) [11][12][13][14][15][16]. This method involves a coupling between the indirect boundary element method (BEM) and the MFS.…”