Average Source Boundary Node Method For Steady-State And Transient Nonhomogeneous And Nonlinear Problems

The Boundary Element Method has become an effective alternative to the domain method,such as the Finite Difference Method and the Finite Element Method,especially in cases where high precision requirements or domain methods cannot be completed,such as infinite domains.However,the most important feature of a boundary element is that it only needs to discretize the boundary rather than the domain.This advantage is especially important for programming because it involves shape modification to complete recombination,which is difficult to implement with finite element methods.The differential equations known for many basic solutions,as well as some interesting engineering problems,can be successfully solved by the boundary element method,including acoustics,elastic mechanics,and potential problems.However,when the basic solution cannot be determined or it is too complicated,it is difficult to calculate with the boundary element,and the estimation of the value is impractical at this time.When we encounter non-homogeneous bodies with variable coefficients and nonlinear problems,the basic solutions are usually indeterminate except for special problems.At this time,we cannot use traditional methods for numerical simulation.The average source boundary node method overcomes the limitations of the traditional method and is a kind of pure boundary-type meshless method.It combines the average source method and the regularized boundary integral equation without any unit and integral,and avoids singularity problem.In solving complex heterogeneous and nonlinear problems,this paper develops the average source boundary node method,coupling the analog equation method and the radial basis function,transforming the original problem into a basic solution known,but the virtual source is unknown.An additional field is introduced,the problem is transformed into a global approximation based on the radial basis function,and then its numerical solution is estimated from the known basic solution.The article method is tested by numerical examples.The numerical simulation of two-dimensional and three-dimensional heterogeneity problems is carried out,and the two-dimensional and three-dimensional nonlinear problems and heat conduction transient problems are studied.The average source boundary node method is used to solve the non-homogeneity problem.The feasibility of homogenization and nonlinear problems,and the calculation accuracy is good and the program design is simple.