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Showing 1 to 20 of 22 for “"Adjoint equations"”.
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Computational Solutions of the Forward and Adjoint Euler Equations with Application to Duct Aeroacoustics
… are performed in this study. In addition, the adjoint equations for the linearized Euler equations in the time domain are formulated for the Cartesian coordinates Analytical solution for adjoint equations is derived by using Green's function in 2D and 3D. The derivation of reciprocal relations …
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Gradient-Based Optimum Aerodynamic Design Using Adjoint Methods
Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin’s Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the …
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Sensitivities in Option Pricing Models
… cost function. In this thesis we highlight the adjoint method for computing gradients of the cost function in the context of gradient based optimization and show its importance. We derive the continuous adjoint equations with appropriate boundary conditions for three main option pricing models: …
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A Parallel-In-Time Gradient-Type Method For Optimal Control Problems
… requires the forward solution of the state equations followed by the backward solution of the adjoint equations before the gradient can be computed and the controls can be updated. The solution of the state equations and the adjoint equations is computationally expensive, is carried out …
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Sensitivity analysis and optimization in low order thermoacoustic models
… thesis a wave-based network model is used. Using adjoint methods the gradients of the eigenvalue with respect to system parameters can be obtained at a low computational cost. This information is used as an input to an optimization routine to find stable thermoacoustic configurations. In this …
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Characterization of Subsurface Heterogeneity Using Transient Hydraulic and Tracer Tomography
… aquifer.Our SSLE approach involves solving adjoint equations during the sensitivity analysis for transient flow, which creates greater computational cost than steady state hydraulic tomography. To reduce the computational cost, we developed an estimation approach that utilizes the zeroth and …
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Centrifugal compressor return channel shape optimization using adjoint method
… gradient-based optimization process using the adjoint method and its application to centrifugal compressor return channel loss reduction. A proper objective function definition and a generalized geometry parametrization and manipulation algorithm were developed, and the appropriate adjoint …
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Shape optimization theory and applications in hydrodynamics
… are observed to yield identical solutions and adjoint equations. Two alternative ways are considered for determining the variation of the objective functional with respect to the state variable which is required to solve the adjoint equation defined on the body boundary. Comparison of these two …
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Fréchet Sensitivity Analysis and Parameter Estimation in Groundwater Flow Models
… problem, then addressed with algorithms based on adjoint equations, quasi-Newton schemes, and multilevel optimization. In addition to the parameter estimation problem, we consider properties of the parameter to solution map. This includes invertibility (known as identifiability) and …
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Coupled Adjoint-based Sensitivity Analysis using a FSI Method in Time Spectral Form
A time spectral and coupled adjoint based sensitivity analysis of rotor blade is carried out in this study. The time spectral method is an efficient technique to solve unsteady periodic problems by transforming unsteady equation of motion to a steady state one. Due to the availability of the …
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Aerodynamic Design Sensitivities on an Unstructured Mesh Using the Navier-Stokes Equations and a Discrete Adjoint Formulation
A discrete adjoint method is developed and demonstrated for aerodynamic design optimization on unstructured grids. The governing equations are the three-dimensional Reynolds-averaged Navier-Stokes equations coupled with a one-equation turbulence model. A discussion of the numerical implementation …
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Maneuver and control of flexible spacecraft
… simultaneously suppressing any vibrations. The equations of motion for a three-dimensional spacecraft undergoing large rigid-body maneuvers are derived. The elastic motions are assumed to remain in the linear range. A method of substructure synthesis is presented which spatially discretizes the …
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Optimal Control Modeling and Simulation, with Application to Cholera Dynamics
… optimal control system that involves the state equations, the adjoint equations, and the optimality condition that characterizes the controls. The system is then numerically solved using an iterative procedure based on the Forward-Backward Sweep Method. We discuss in detail the mathematical …
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Adjoint-based optimization for hyperbolic balance laws in the presence of discontinuities
… optimization in multiphase flows using discrete adjoint-based methods. The main issues we will endeavor to study are the impact on the linearized and adjoint equations of discontinuous solutions, the behavior of the THINC-family of numerical schemes under linearization and the rigorous …
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Viscosity stabilized adjoint method for unsteady compressible Navier-Stokes equations
… finalizing the flow parameters of a system. The adjoint method accelerates the design process by providing gradients of the design objective with respect to the system parameters. But, typically, adjoint-based design optimization methods have used low fidelity simulations like Reynolds Averaged …
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Methods for Analysis of Nonlinear Thermoacoustic Systems
… other than those used to form the governing equations. Once the limit cycles are found, these continuation methods track them as the operating condition of the system changes. Most continuation methods are impractical for finding limit cycles in large thermoacoustic systems because the …
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Multi-parameter estimation in glacier models with adjoint and algorithmic differentiation
… Efficient computation of the tangent linear and adjoint models give researchers easy access to model derivatives. The adjoint and tangent linear models enable efficient global sensitivity computation and parameter optimization on unknown or uncertain ice sheet properties, information used to …
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Variational Methods in Ice Sheet Modelling
… usually necessary to make approximations to the equations governing ice flow. At the same time, it is important to have an understanding of the specific assumptions that lead to these approximations. We develop a variational principle for Stokes flow, and neglect certain components in order to …
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Variational Methods in Ice Sheet Modelling
… usually necessary to make approximations to the equations governing ice flow. At the same time, it is important to have an understanding of the specific assumptions that lead to these approximations. We develop a variational principle for Stokes flow, and neglect certain components in order to …
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Advances in Symbolic Regression: From Generalized Formulation to Density Estimation and Inverse Problem
… of recovering underlying partial differential equations (PDEs) from data through the use of the adjoint method. We begin by considering a family of parameterized PDEs encompassing linear, nonlinear, and spatial derivative candidate terms. We then formulate a PDE-constrained optimization problem …
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