Second-order adjoint sensitivity analysis methodology (2nd-asam) for large-scale nonlinear systems: II. Application to a nonlinear heat conduction benchmark
For large-scale nonlinear systems, this method enables efficient computation of second-order sensitivities without modifying the solver, which is crucial for uncertainty quantification and optimization.
The paper applies the 2nd-ASAM method to a nonlinear heat conduction benchmark, computing all 1st- and 2nd-order derivatives of the temperature response with respect to five parameters using only six adjoint computations, while keeping the differential operator unchanged.
This work presents an illustrative application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci (2015) to a paradigm nonlinear heat conduction benchmark, which models a conceptual experimental test section containing heated rods immersed in liquid lead-bismuth eutectic. This benchmark admits an exact solution, thereby making transparent the underlying mathematical derivations. For this illustrative problem, six large-scale adjoint computations sufficed to compute exactly all five 1st-order and fifteen distinct 2nd-order derivatives of the temperature response to the five model parameters. Very significantly, only the sources on the right-sides of the heat conduction differential operator need to be modified; the left-side of the differential equations (and hence the solver in large-scale practical applications) remains unchanged.