Techniques for Solving Inverse Heat Transfer Problems

This chapter provides the necessary mathematical background needed in the use of some powerful techniques for solving inverse heat transfer problems. The following four techniques are considered: Levenberg-Marquardt Method for Parameter Estimation, Conjugate Gradient Method for Parameter Estimation, Conjugate Gradient Method with Adjoint Problem for Parameter Estimation and Conjugate Gradient Method with Adjoint Problem for Function Estimation. Technique one is quite efficient for solving linear and nonlinear parameter estimation problems. However, difficulties may arise in nonlinear estimation problems involving a large number of unknown parameters, because of the time spent in the computation of the sensitivity matrix. The Levenberg-Marquardt method, originally devised for application to nonlinear parameter estimation problems, has also been successfully applied to the solution of linear problems that are too ill-conditioned to permit the application of linear algorithms. Technique II, the Conjugate Gradient Method, is a straightforward and powerful iterative technique for solving linear and nonlinear inverse problems of parameter estimation.