The author has achieved the breakthrough of generalizing the First-Order Theory presented in his previous books, to the efficient computations of arbitrarily high-order sensitivities for nonlinear systems (HONASAP). This breakthrough has many applications, especially when there is a need to quantify nonlinear behavior.
Autorentext
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.
Klappentext
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.
Zusammenfassung
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.
Inhalt
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