TITLE:
Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response
AUTHORS:
Dan Gabriel Cacuci
KEYWORDS:
Second-Order Adjoint Comprehensive Sensitivity Analysis Methodology (2nd-CASAM), Evolution Benchmark Model, Exact and Efficient Computation of First- and Second-Order Response Sensitivities
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.10 No.3,
July
22,
2020
ABSTRACT: This work illustrates the application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response is the value of the model’s state function (particle concentration or particle flux) at a point in phase-space, which would simulate a pointwise measurement of the respective state function. This paradigm model admits exact closed-form expressions for all of the 1st- and 2nd-order response sensitivities to the model’s uncertain parameters and domain boundaries. These closed-form expressions can be used to verify the numerical results of production and/or commercial software, e.g., particle transport codes. Furthermore, this paradigm model comprises many uncertain parameters which have relative sensitivities of identical magnitudes. Therefore, this paradigm model could serve as a stringent benchmark for inter-comparing the performances of all deterministic and statistical sensitivity analysis methods, including the 2nd-CASAM.