A boundary element-based inverse-problem in estimating transient boundary conditions with conjugate gradient method

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 transient boundary temperatures in a multi-dimensional domain 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 per cent conÞdence bound is thus obtained. Finally, the e¤ects of the measurement errors to the inverse solutions are discussed. Results show that the advantages of applying the CGM in the inverse calculations lie in that (i) the major di¦culties in choosing a suitable quadratic norm, determining a proper regularization order and determining the optimal smoothing (or regularization) coe¦cient in the RM are avoided and (ii) it is less sensitive to the measurement errors, i.e. more accurate solutions are obtained