A Meshless Projection Iterative Method For Unilateral Problems

The unilateral problems are the kinds of mathematical physics problems which appear in variational inequalities. Such as electroplating problem, obstacle problem, groundwater flow problem are the unilateral problems in science and engineering problems. In some numerical calculations, meshless methods eliminate the difficulty of meshing, it is applied widely, it is also a new method which solute partial differential equation boundary problems. This paper is using the meshfree projection iteration method to solve the unilateral problems.The first chapter reviews the recent developments of the unilateral problems, then lead our intention is combine the meshless projection iteration method with the boundary integral equation method of meshless boundary, to use meshless interpolation boundary meshless projection iteration method to solve the unilateral problems.The second chapter is the core part of this paper, in this part we describe the projection iterative algorithm of unilateral problems. First of all, we use an interpolating moving least-squares scheme for constructing interpolation functions, then a projection operator is used to formulate the boundary integral equations and the formulate of interpolating boundary element-free method are obtained for unilateral problems, summarize the algorithm steps, finally, the convergence of the developed meshless method is derived mathematically.The third chapter, the capability of the method is also illustrated and assessed through some numerical examples, meanwhile, we find the method has good convergence, less iteration, the computation time is relatively small, the numerical solution and the exact solution is consistent.The fourth chapter gives relevant summary, describe the meshfree projection iteration method is an effective method to solve the model for the unilateral problems and it is good for the engineering applications.