The Second-Order Adjoint Sensitivity Analysis Methodology: 1st Edition (Hardback) book cover

The Second-Order Adjoint Sensitivity Analysis Methodology

1st Edition

By Dan Gabriel Cacuci

Chapman and Hall/CRC

306 pages | 95 B/W Illus.

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pub: 2018-02-28
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Description

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.

Table of Contents

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

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.

About the Series

Advances in Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT004000
MATHEMATICS / Arithmetic