Dual reciprocity boundary element analysis of inverse heat conduction problems

Abstract

This paper presents an application of the dual reciprocity boundary element method (DRBEM) to inverse heat conduction problems. To deal with the ill-posed nature of the problem, iterative regularization methods of conjugate gradient type have been used. Preconditioned biconjugate (PBCG) method has been used for the solution if the discretized boundary element system has as many equations as the total number of unknowns. Preconditioned conjugate gradient (PCG) method has been utilized for the general case in which more equations are available than unknowns. Numerical results show that PBCG algorithm is useful only for inverse problems having unspecified boundary conditions on a small fraction of the boundary, whereas the PCG algorithm works well for any problem. Flux estimates with both the methods are seen to be sensitive to the location of measurement points and measurement errors. In contrast, temperature estimates are very accurate, nearly insensitive to measurement errors, and only weakly sensitive to location of measurement points. Further, constant elements work much better than the linear elements in terms of accuracy as well as stability of the numerical solution, and should be preferred in DRBE analysis of inverse heat conduction problems.