Table of Contents:
  • MOTIVATION FOR COMPUTING FIRST- AND SECOND-ORDER SENSITIVITIES OF SYSTEM RESPONSES TO THE SYSTEMS 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.