TRANSIENT INVERSE HEAT-CONDUCTION PROBLEM SOLUTIONS VIA NEWTONS METHOD

Analytical first and second-order sensitivities are derived for a gene ral, transient nonlinear problem and are then used to solve an inverse heat conduction problem (IHCP). The inverse analyses use Newton's met hod to minimize an error function which quantifies the discrepancy bet ween the experimental and predicted responses. These Newton results ar e compared to results obtained from the first-order variable metric Br oyton-Fletcher-Goldfarb-Shanno (BFGS) method. Inverse analyses are per formed for both linear and nonlinear thermal systems. For linear syste ms, Newton's method converges in one iteration. For nonlinear systems, Newton's method sometimes diverges apparently due to a small radius o f convergence. In these cases a combined BFGS-Newton's method is used to solve the IHCP. The unknown data fields are parameterized via the e igen basis of the Hessian to illustrate the need for regularization. R egularization is then incorporated and the IHCP is solved with Newton' s method. All heat transfer analyses and sensitivity analyses are perf ormed via the finite element method. (C) 1997 Elsevier Science Ltd.