Average Source Boundary Node Method For Inverse Identification Of Boundary Conditions

The average source boundary node method(ASBNM)is a recent boundary-type meshless method,which uses only the boundary nodes in the solution procedure without involving any element or integration notion,that is truly meshless and easy to implement.Rceently,boundary-type meshless method mainly included two categories:one is the meshless method based on the basic solution,which often leads to ill-conditioned system matrix;the other is the combined boundary integral equation and moving least square(LS)meshless method,which still needs to calculate the integral.Different from the previous work,the ASBNM is based on the completely regularized boundary integral equation and the source average technique(AST).The singularity of the coincident source-collocation nodes in fundamental solution is removed by using the completely regularized boundary integral equation,and then the element and integral are avoided.This paper firstly attempts to deal with the ASBNM for the inverse problem of boundary conditions.It is well known that numerical solutions to inverse problems could lead to ill-posed linear systems,included the ASBNM.So we can use the truncated singular value decomposition(TSVD)and the Tikhonov(TR)regularization techniques with the generalized cross validation(GCV)criterion are employed to solve the problem.Three benchmark numerical examples indicate that the proposed method is computationally efficient and numerically stable for the solution of the inverse problems of Cauchy heat conduction.In this work:(1)In chapter three,the ASBNM for two-dimensional inverse potential problem is studied.(2)In chapter four,the ASBNM for three-dimensional inverse potential problem is studied.(3)In chapter five,the ASBNM for three-dimensional inverse anisotropic problem is studied.