Książki

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.

The Second-Order Adjoint Sensitivity Analysis Methodology

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