The method of fundamental solutions for Signorini problems

Abstract

We investigate the use of the method of fundamental solutions (MFS) for the numerical solution of Signorini boundary value problems. The MFS is an ideal candidate for solving such problems because inequality conditions alternating at unknown points of the boundary can be incorporated naturally into the least-squares minimization scheme associated with the MFS. To demonstrate its efficiency, we apply the method to two Signorini problems. The first is a groundwater flow problem related to percolation in gently sloping beaches, and the second is an electropainting application. For both problems, the results are in close agreement with previously reported numerical solutions.