Regularization Algorithm Of Inverse Identification Of Boundary Conditions For2-D Potential Problems

The concept, classification and research status of ill-posed inverse problemsare introduced. The research advance of the boundary condition inverseidentification problem is reviewed.The principle of singular value decomposition(SVD), generalized SVD andTikhonov regularization method is presented. The regularization parameter choosemethods, such as L-curve method, GCV, Quasi-optimality criterion and Morozovdiscrepancy principle, are discussed.The boundary integral equation for2D potential problems and the discretisedBEM process are deduced. For2D boundary condition identification potentialproblems with isotropic materials, Tikhonov regularization method is proposed.L-curve method is applied to choose regularization parameter. The problems withpartially given boundary conditions and physical quantities at inner points areanalyzed. Truncated SVD method can also solve the problem.The analytical integral algorithm and SVD are applied to treat2-D orthotropicpotential Cauchy problems of thin body. The nearly singular integrals in the BEMfor thin body problems are evaluated by the analytical integral formulas. Thesystem equation is solved by the TSVD. The undulating-curve method for fluxsolutions is proposed to select the truncated number associated with useful singularvalues.The numerical results of the typical examples demonstrate that Tikhonovregularization method and TSVD method are effective to treat2D boundaryconditions identification potential problems.