1st Edition

The Second-Order Adjoint Sensitivity Analysis Methodology

By Dan Gabriel Cacuci Copyright 2018
    326 Pages 95 B/W Illustrations
    by Chapman & Hall

    326 Pages 95 B/W Illustrations
    by Chapman & Hall

    The Second-Order Adjoint Sensitivity Analysis Methodology generalizes the First-Order Theory presented in the author’s previous books published by CRC Press. This breakthrough has many applications in sensitivity and uncertainty analysis, optimization, data assimilation, model calibration, and reducing uncertainties in model predictions. The book has many illustrative examples that will help readers understand the complexity of the subject and will enable them to apply this methodology to problems in their own fields.

    Highlights:

    • Covers a wide range of needs, from graduate students to advanced researchers

    • Provides a text positioned to be the primary reference for high-order sensitivity and uncertainty analysis

    • Applies to all fields involving numerical modeling, optimization, quantification of sensitivities in direct and inverse problems in the presence of uncertainties.

    About the Author:

    Dan Gabriel Cacuci is a South Carolina SmartState Endowed Chair Professor and the Director of the Center for Nuclear Science and Energy, Department of Mechanical Engineering at the University of South Carolina. He has a Ph.D. in Applied Physics, Mechanical and Nuclear Engineering from Columbia University. He is also the recipient of many awards including four honorary doctorates, the Ernest Orlando Lawrence Memorial award from the U.S. Dept. of Energy and the Arthur Holly Compton, Eugene P. Wigner and the Glenn Seaborg Awards from the American Nuclear Society.

     

    MOTIVATION FOR COMPUTING FIRST- AND SECOND-ORDER SENSITIVITIES OF SYSTEM RESPONSES TO THE SYSTEM’S PARAMETERS 

    The Fundamental Role of Response Sensitivities for Uncertainty Quantification 

    The Fundamental Role of Response Sensitivities for Predictive Modeling

    Advantages and Disadvantages of Statistical and Deterministic Methods for Computing Response Sensitivities

    ILLUSTRATIVE APPLICATION OF THE SECOND-ORDER ADJOINT SENSITIVITY ANALYSIS METHODOLOGY (2nd-ASAM) TO A LINEAR EVOLUTION PROBLEM 

    Exact Computation of the 1st-Order Response Sensitivities 

    Exact Computation of the 2nd-Order Response Sensitivities

    Computing the 2nd-Order Response Sensitivities Corresponding to the 1st-Order Sensitivities

    Discussion of the Essential Features of the 2nd-ASAM

    Illustrative Use of Response Sensitivities for Predictive Modeling

    THE SECOND-ORDER ADJOINT SENSITIVITY ANALYSIS METHODOLOGY (2nd-ASAM) FOR LINEAR SYSTEMS 

    Mathematical Modeling of a General Linear System 

    The 1st-Level Adjoint Sensitivity System (1st-LASS) for Computing Exactly and Efficiently 1st-Order Sensitivities of Scalar-Valued Responses for Linear Systems

    The 2nd-Level Adjoint Sensitivity System (2nd-LASS) for Computing Exactly and Efficiently 1st-Order Sensitivities of Scalar-Valued Responses for Linear Systems

    APPLICATION OF THE 2nd-ASAM TO A LINEAR HEAT CONDUCTION AND CONVECTION BENCHMARK PROBLEM

    Heat Transport Benchmark Problem: Mathematical Modeling

    Computation of First-Order Sensitivities Using the 2nd-ASAM

    Computation of first-order sensitivities of the heated rod temperature

    Computation of first-order sensitivities of the coolant temperature

    Verification of the "ANSYS/FLUENT Adjoint Solver"

    Applying the 2nd-ASAM to Compute the Second-Order Sensitivities and Uncertainties for the Heat Transport Benchmark Problem

    APPLICATION OF THE 2nd-ASAM TO A LINEAR PARTICLE DIFFUSION PROBLEM

    Paradigm Diffusion Problem Description

    Applying the 2nd-ASAM to Compute the First-Order Response Sensitivities to Model Parameters

    Applying the 2nd-ASAM to Compute the Second-Order Response Sensitivities to Model Parameters 

    Role of Second-Order Response Sensitivities for Quantifying Non-Gaussian Features of the Response Uncertainty Distribution

    Illustrative Application of First-Order Response Sensitivities for Predictive Modeling

    APPLICATION OF THE 2nd-ASAM FOR COMPUTING SENSITIVITIES OF DETECTOR RESPONSES TO UNCOLLIDED RADIATION TRANSPORT

    The Ray-Tracing Form of the Forward and Adjoint Boltzmann Transport Equation

    Application of the 2nd-ASAM to Compute the First-Order Response Sensitivities to Variations in Model Parameters

    Application of the 2nd-ASAM to Compute the Second-Order Response Sensitivities to Variations in Model Parameters

    THE SECOND-ORDER ADJOINT SENSITIVITY ANALYSIS METHODOLOGY (2nd-ASAM) FOR NONLINEAR SYSTEMS

    Mathematical Modeling of a General Nonlinear System

    The 1st-Level Adjoint Sensitivity System (1st-LASS) for Computing Exactly and Efficiently the 1st-Order Sensitivities of Scalar-Valued Responses 

    The 2nd-Level Adjoint Sensitivity System (2nd-LASS) for Computing Exactly and Efficiently the 2nd-Order Sensitivities of Scalar-Valued Responses for Nonlinear Systems

    APPLICATION OF THE 2nd-ASAM TO A NONLINEAR HEAT CONDUCTION PROBLEM

    Mathematical Modeling of Heated Cylindrical Test Section

    Application of the 2nd-ASAM for Computing the 1st-Order Sensitivities

    Application of the 2nd-ASAM for Computing the 2nd-Order Sensitivities

    Biography

    Dan Gabriel Cacuci is a South Carolina SmartState Endowed Chair Professor and the Director of the Center for Nuclear Science and Energy, Department of Mechanical Engineering at the University of South Carolina. He has a Ph.D. in Applied Physics, Mechanical and Nuclear Engineering from Columbia University. He is also the recipient of many awards including four honorary doctorates, the Ernest Orlando Lawrence Memorial award from the U.S. Dept. of Energy and the Arthur Holly Compton, Eugene P. Wigner and the Glenn Seaborg Awards from the American Nuclear Society.