%0 Journal Article
%T Illustrative Application of the 2<sup>nd</sup>-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response
%A Dan Gabriel Cacuci
%J American Journal of Computational Mathematics
%P 355-381
%@ 2161-1211
%D 2020
%I Scientific Research Publishing
%R 10.4236/ajcm.2020.103019
%X This work illustrates the application of the ¡°Second Order Comprehensive Adjoint Sensitivity Analysis Methodology¡± (2<sup>nd</sup>-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 1<sup>st</sup>- and 2<sup>nd</sup>-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 2<sup>nd</sup>-CASAM.
%K Second-Order Adjoint Comprehensive Sensitivity Analysis Methodology (2&lt
%K sup&gt
%K nd&lt
%K /sup&gt
%K -CASAM)
%K Evolution Benchmark Model
%K Exact and Efficient Computation of First- and Second-Order Response Sensitivities
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=101648