A boundary-element-based inverse problem of estimating boundary conditions in an irregular domain with statistical analysis

A boundary-element-method (BEM)-based inverse algorithm utilizing the iterative regularization method, i.e., the conjugate gradient method (CGM), is used to solve the inverse heat conduction problem (IHCP) of estimating the unknown boundary temperature in a multidimensional steady-state problem with arbitrary geometry. The results obtained by the CGM are compared with that obtained by the standard regularization method (RM).The error estimation based on the statistical analysis is derived from the formulation of the RM. A 99% confidence bound is thus obtained. Finally, the effects of the measurement errors on the inverse solutions are discussed. The present technique can be easily extended to the transient heat conduction problem.Results show that the advantages of applying the CGM in the inverse calculations lie in that (I) the major difficulties in choosing a suitable form of quadratic norm, determining a proper regularization order, and determining the optimal smoothing (or regularization) coefficient in the RM are avoided, and (2) it is less sensitive to measurement errors—i.e., more accurate solutions are obtained for the numerical examples illustrated here.