MFS-MPS Method For The Second Kind Of Elliptic Variational Inequality Problems And Convergence Analy

The Method of Fundamental Solutions(MFS)is a strong form of boundary type meshless method for solving homogeneous problems,which has the advantages of simple form,easy program implementation and high accuracy.It has been widely used in the field of engineering calculation.However,the theoretical analysis of this method is insufficient and there is little involvement in the problem of variational inequalities.In this paper,the MFS-MPS method for the Poisson problem with mixed boundary conditions and the second kind of elliptic variational inequality problem is constructed by combining the Method of Particular Solutions(MPS)and MFS methods,and the complete theoretical analysis is given,and numerical examples are realized:Theoretical analysis and numerical examples of MFS-RPF-PS method for linear elastic statics problems with physical strength;Theoretical analysis and numerical examples of the MFS of the static simplified Coulomb friction contact problem.The main work of this paper is as follows:In the second chapter,MFS of Laplace problem with mixed boundary conditions is given,and its error estimate is derived;Then,combined with MPS method,the MFS-MPS method for Poisson problem with mixed boundary conditions is constructed,and a complete theoretical analysis is given.Finally,numerical experiments are carried out to verify the feasibility and effectiveness of the method and theoretical analysis.In the third chapter,we study the MFS-MPS method for the second kind of elliptic variational inequality problems.At first,the mathematical description of this kind of problem and its equivalent variational inequality form are given.It is transformed into a saddle point problem by Uzawa dual method,and the computational form is given by combining MFS-MPS method and Uzawa algorithm.The detailed process of algorithm implementation is given;Secondly,the error estimates of the MFS-MPS method for the second kind of elliptic variational inequality problems are derived.Finally,two numerical examples are implemented to verify the feasibility of the method and the effectiveness of the error estimates.In the fourth chapter,the MFS-RBF-PS method for linear elastic static problems with physical forces and the MFS method of statically simplified Coulomb frictional contact problems are studied.Firstly,the preliminary knowledge and mathematical description of linear elastic statics are given,and then the detailed implementation process of the algorithm is given.The error estimates of the MFS-RBF-PS method for linear elastic statics with physical force are derived.Secondly,the mathematical description of the static simplified Coulomb friction contact problem and its equivalent variational inequality form are described.The Uzawa dual method is used to transform it into a saddle point problem.The calculation format is given by combining the basic solution with the Uzawa algorithm.The error estimation of the MFS of the static simplified Coulomb friction contact problem is derived.Finally,the numerical examples are implemented to verify the feasibility of the method and the effectiveness of the error estimation.