ABSTRACT
This chapter illustrates the main steps for implementing the second order adjoint sensitivity analysis methodology (2nd-ASAM) by using a simple evolution model that admits a closed-form, easily tractable, analytical solution. Furthermore, this paradigm illustrative model comprises sufficiently many parameters, just as typically found in realistic physical systems, to preclude the use of statistical and or other deterministic methods for computing exactly all of the first- and second-order response sensitivities. The chapter also illustrates the principles underlying the 2nd-ASAM for linear systems by applying it to compute the first and second-order sensitivities of the response defined for the paradigm model. The expressions of the second-order response sensitivities are provided by the Gateaux differentials of the expressions. It is important to note that many of the mixed second-order sensitivities are obtained twice, stemming from distinct second-level adjoint sensitivity system.
