Regularized BEM With Indirect Unknowns For Inverse Identification Of Boundary Conditions For 2D Potential And Elasticity Problems

Inverse problem in mathematical physics is widely used in engineering,and inverse identification of boundary conditions problem is a classical inverse problem.Anisotropic structure has the characteristics that heat transfer coefficients change with directions.With the development of science and technology,the application of new materials has been more and more extensive in practical engineering.Therefore the development of numerical methods for this problem has numerous significance.Finite Difference Method(FDM)and Finite Element Method(FEM)are commonly used in numerical calculation.But generation and inspection of the mesh exhibit are difficult and are both laborious and time consuming.The boundary element method(BEM)only needs to discretize the boundary of the body,making the numerical modeling easily.At present,the study of inverse problems have been focused on direct boundary element method,related to the 2D potential and elasticity identification boundary conditions problems.This paper is engaged in the indirect boundary element method for 2D potential and elasticity inverse problems.In this work,the BEM for 2D potential and elasticity identification boundary conditions problems are studied in chapter three and four.Then the anisotropy thin body structure inverse problems are investigated in chapter five.The ill-conditioned linear system of equations discreted by the BEM is solved by TSVD method and the Tikhonov regular method.And the parameters used in TSVD and Tikhonov are determined by the L-curve and GCV method,good effect has been achieved.Numerical results indicate that the proposed method is accurate and stable.Effective results can be achieved when noise existed.In a word,our work expands the scope of application of BEM and provides a new and effective numerical method for inverse problems.