American Journal of Computational Mathematics

Volume 10, Issue 3 (September 2020)

ISSN Print: 2161-1203   ISSN Online: 2161-1211

Google-based Impact Factor: 1.05  Citations  

Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response

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DOI: 10.4236/ajcm.2020.103020    327 Downloads   737 Views  Citations
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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.

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Cacuci, D. (2020) Illustrative Application of the 2nd-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Reaction-Rate Detector Response. American Journal of Computational Mathematics, 10, 382-397. doi: 10.4236/ajcm.2020.103020.

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