Radial Basis Method For Nonhomogeneous Nonlinear Steady-State And Transient Problems

Due to the shortcomings of the finite element method,such as the need for area division,the boundary element method has risen rapidly.This type of calculation method,which does not require area division and only requires discrete boundaries,is relatively simple to operate and has high accuracy.Instead of the finite element method,it is widely used in the fields of elasticity and potential.However,when using the boundary element to solve a problem,it is necessary to rely on the basic solution for numerical calculations.When the basic solution cannot be determined,for example,some heterogeneous problems with varying coefficients,the boundary element method cannot continue to play a role.Radial basis function method,as an emerging interpolation approximation technology,can effectively avoid the shortcomings of the boundary element method,has the advantages of simple operation,easy implementation,and is not affected by the problem dimension and problem area,and its accuracy is usually Satisfactory.Therefore,more and more scientists have applied the radial basis function method to problems such as computational mechanics and fluid dynamics.However,when the radial basis function method is used to deal with the problem,the numerical results are greatly affected by its shape parameters.In general,as the shape parameter value increases,the accuracy of the approximate solution continues to increase;however,when the shape parameter is large enough,the resulting numerical matrix may have a considerable number of condition numbers,which cannot be solved smoothly,resulting in numerical instability and loss of precision.A new radial basis function is proposed in Ref.[26],which greatly reduces the influence of the shape parameters on the numerical results,and even makes the calculation results unaffected,thereby increasing the value interval of the shape parameters and increasing The stability of the method.This paper extends the new radial basis function constructed in Ref.[26] to non-homogeneous,nonlinear problems and transient problems.The specific work of this article is:(1)In chapter 3,we researched the radial basis function method for heterogeneous problems.(2)In chapter 4,we researched studies the radial basis function method for nonlinear problems.(3)In chapter 5,we researched the radial basis function method for transient problems.