Second-order adjoint sensitivity analysis methodology (2nd-asam) for large-scale nonlinear systems: II. Application to a nonlinear heat conduction benchmark

Abstract

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.

arXiv admin note: text overlap with arXiv:1411.6158

References in corpus (3)

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• Second-order adjoint sensitivity analysis procedure (SO-ASAP) for computing exactly and efficiently first- and second-order sensitivities in large-scale linear systems:II. Illustrative application to a paradigm particle diffusion problem
• Second-order adjoint sensitivity analysis methodology (2nd-asam) for large-scale nonlinear systems: I. Theory