TITLE:
Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate 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
24,
2020
ABSTRACT: This work continues the illustrative application of the “Second Order Comprehensive Adjoint Sensitivity Analysis Methodology” (2nd-CASAM) to a benchmark mathematical model that can simulate the evolution and/or transmission of particles in a heterogeneous medium. The model response considered in this work is a reaction-rate detector response, which provides the average interactions of particles with the respective detector or, alternatively, the time-average of the concentration of a mixture of substances in a medium. The definition of this model response includes both uncertain boundary points of the benchmark, thereby providing both direct and indirect contributions to the response sensitivities stemming from the boundaries. The exact expressions for the 1st- and 2nd-order response sensitivities to the boundary and model parameters obtained in this work can serve as stringent benchmarks for inter-comparing the performances of all (deterministic and statistical) sensitivity analysis methods.