A meshfree method for Signorini problems using boundary integral equations (Q1718514)

Summary: This paper presents a meshfree method for the numerical solution of Signorini problems. In this method, a projection iterative algorithm is used to convert the boundary inequality constraints into a fixed point equation. Then, the boundary value problem is reformulated as boundary integral equations and the unknown boundary variables are interpolated by the point interpolation scheme. Thus, only a nodal data structure on the boundary of a domain is required, and boundary conditions can be implemented directly and easily. The convergence of this method is verified theoretically. Numerical examples involving groundwater flow and electropainting problems are also provided to illustrate the performance and usefulness of the method.