Ch. Huang et Cw. Chen, A BOUNDARY-ELEMENT-BASED INVERSE PROBLEM OF ESTIMATING BOUNDARY-CONDITIONS IN AN IRREGULAR DOMAIN WITH STATISTICAL-ANALYSIS, Numerical heat transfer. Part B, Fundamentals, 33(2), 1998, pp. 251-268
A boundary-element-method (BEM)-based inverse algorithm utilizing the
iterative regularization method i.e., the conjugate gradient method (C
GM) is used to solve the inverse heat conduction problem (IHCP) of est
imating 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 ire standard regularization method
(RM). The error estimation based on the statistical analysis is deriv
ed from the formulation of the RM. A 99% confidence bound is thus obta
ined. Finally, the effects of the measurement errors on the inverse so
lutions are discussed. The present technique can be easily extended to
the transient heat conduction problem.Results show that the advantage
s of applying the CGM in the inverse calculations lie in that (1) the
major difficulties in choosing a suitable form of quadratic norm, dete
rmining a proper regularization order, and determining the optimal smo
othing (or regularization) coefficient in the RM are avoided, and (2)
it is less sensitive to measurement errors--i.e., more accurate soluti
ons are obtained for the numerical examples illustrated here.