In this research, the continuous adjoint method is applied to optimize an airfoil in subsonic and transonic flows. An Euler flow solver is used to analyze the inviscid compressible flow over airfoils in each design cycle. Two design problems appearing in aerodynamic shape optimization, namely inverse pressure design and drag minimization were investigated. In the first part, a test case was car...

A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are discussed and used to determine the periodic, compressible, viscous flow around a 2D flapping airfoil. The Newton-Krylov method uses matrix-free GMRES to solve the linear systems of equations that arise in the nonlinear...

1. Abstract This paper presents a topology optimization method using the lattice Boltzmann method for the design of a flow channel considering two-phase fluid flows. This approach enables the design of fluidic devices such as two-phase microchannels that achieve a desired flow with maximal performances such as mixing and reaction, and extraction efficiencies. The optimization problems are formu...

An e4cient numerical method for sensitivity computation of large-scale di$erential-algebraic systems is developed based on the adjoint method. Issues that are critical for the implementation are addressed. Complexity analysis and numerical results demonstrate that the adjoint sensitivity method is advantageous over the forward sensitivity method for applications with a large number of sensitivi...

We use C *-algebra theory to provide a new method of decomposing the essential spectra of self-adjoint and non-self-adjoint Schrödinger operators in one or more space dimensions.

We propose elastic isotropic wavefield tomography formulated with the misfit of observed and recorded data as the objective function. The adjoint-state method enables efficient calculation of the gradient of this data misfit function. We solve this optimization problem with the gradient-descent method in order to update the model parameters iteratively. Using the elastic isotropic wave-equation...

We consider the resolution of an inverse problem for the identification of some reduced nonlinear diffusive models. The modal identification method is dealt with along with a gradient-type optimization method. Two distinct approaches are considered and compared. On one hand the classical finite differences approach and, on the other hand, the adjoint method for the computation of the objective ...

S U M M A R Y We compare finite-frequency phase and amplitude sensitivity kernels calculated based on frequency-domain surface wave mode summation and a time-domain adjoint method. The adjoint calculations involve a forward wavefield generated by an earthquake and an adjoint wavefield generated at a seismic receiver. We determine adjoint sources corresponding to frequency-dependent phase and am...

Recent applications’ needs/desires have motivated efforts to develop approaches for optimizing Monte Carlo calculations for global distributions, such as flux or dose rate distributions (e.g., mesh tallies), as well as response at multiple localized detectors and spectra. Recent efforts at Oak Ridge National Laboratory (ORNL) have led to the development of a variation on the Consistent Adjoint ...

This paper introduces and analyzes a new parallel-in-time gradient type method for the solution of convex linear-quadratic discrete-time optimal control (DTOC) problems. Each iteration of the classical gradient method requires the solution of the forward-in-time state equation followed by the solution of the backward-in-time adjoint equation to compute the gradient. To introduce parallelism, th...