Active Control Evaluation for Spacecraft (ACES)

The Air Force goal is to develop vibration control techniques for large flexible spacecraft by addressing sensor, actuator, and control hardware and dynamic testing. The Active Control Evaluation for Spacecraft (ACES) program will address the Air Force goal by looking at two leading control techniques and implementing them on a structural model of a flexible spacecraft under laboratory testing. The first phase in the ACES program is to review and to assess the High Authority Control/Low Authority Control (HAC/LAC) and Filter accomodated Model Error Sensitivity Suppression (FAMESS) control techniques for testing on the modified VCOSS structure. Appropriate sensors and actuators will be available for use with both techniques; locations will be the same for both techniques. The control actuators will be positioned at the midpoint and free end of the structure. The laser source for the optical sensor is mounted on the feed mast. The beam will be reflected from a mirror on the offset antenna onto the detectors mounted above the shaker table bay. The next phase is to develop an analysis simulation with the control algorithms implemented for dynamics verification. The third phase is to convert the control laws into high level computer language and test them in the NASA-MSFC facility. The final phase is to compile all analytical and test results for performance comparisons

A New Approximation of the Schur Complement in Preconditioners for PDE Constrained Optimization

Saddle point systems arise widely in optimization problems with constraints. The utility of Schur complement approximation is now broadly appreciated in the context of solving such saddle point systems by iteration. In this short manuscript, we present a new Schur complement approximation for PDE constrained optimization, an important class of these problems. Block diagonal and block triangular preconditioners have previously been designed to be used to solve such problems along with MINRES and non-standard Conjugate Gradients respectively; with appropriate approximation blocks these can be optimal in the sense that the time required for solution scales linearly with the problem size, however small the mesh size we use. In this paper, we extend this work to designing such preconditioners for which this optimality property holds independently of both the mesh size and of the Tikhonov regularization parameter \beta that is used. This also leads to an effective symmetric indefinite preconditioner that exhibits mesh and \beta-independence. We motivate the choice of these preconditioners based on observations about approximating the Schur complement obtained from the matrix system, derive eigenvalue bounds which verify the effectiveness of the approximation, and present numerical results which show that these new preconditioners work well in practice

Fast iterative solvers for convection-diffusion control problems

In this manuscript, we describe effective solvers for the optimal control of stabilized convection-diffusion problems. We employ the local projection stabilization, which we show to give the same matrix system whether the discretize-then-optimize or optimize-then-discretize approach for this problem is used. We then derive two effective preconditioners for this problem, the �first to be used with MINRES and the second to be used with the Bramble-Pasciak Conjugate Gradient method. The key components of both preconditioners are an accurate mass matrix approximation, a good approximation of the Schur complement, and an appropriate multigrid process to enact this latter approximation. We present numerical results to demonstrate that these preconditioners result in convergence in a small number of iterations, which is robust with respect to the mesh size h, and the regularization parameter β, for a range of problems

Transition metal impurities in semiconductors

Crystal field theory applied transition metal impurities in semiconductor

Robust Iterative Solution of a Class of Time-Dependent Optimal Control Problems

The fast iterative solution of optimal control problems, and in particular PDE-constrained optimization problems, has become an active area of research in applied mathematics and numerical analysis. In this paper, we consider the solution of a class of time-dependent PDE-constrained optimization problems, specifically the distributed control of the heat equation. We develop a strategy to approximate the (1,1)-block and Schur complement of the saddle point system that results from solving this problem, and therefore derive a block diagonal preconditioner to be used within the MINRES algorithm. We present numerical results to demonstrate that this approach yields a robust solver with respect to step-size and regularization parameter

Fast iterative solution of reaction-diffusion control problems arising from chemical processes

PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs

A hybrid-stress finite element for linear anisotropic elasticity

Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased

Identifying Galaxy Mergers in Observations and Simulations with Deep Learning

Mergers are an important aspect of galaxy formation and evolution. We aim to test whether deep learning techniques can be used to reproduce visual classification of observations, physical classification of simulations and highlight any differences between these two classifications. With one of the main difficulties of merger studies being the lack of a truth sample, we can use our method to test biases in visually identified merger catalogues. A convolutional neural network architecture was developed and trained in two ways: one with observations from SDSS and one with simulated galaxies from EAGLE, processed to mimic the SDSS observations. The SDSS images were also classified by the simulation trained network and the EAGLE images classified by the observation trained network. The observationally trained network achieves an accuracy of 91.5% while the simulation trained network achieves 65.2% on the visually classified SDSS and physically classified EAGLE images respectively. Classifying the SDSS images with the simulation trained network was less successful, only achieving an accuracy of 64.6%, while classifying the EAGLE images with the observation network was very poor, achieving an accuracy of only 53.0% with preferential assignment to the non-merger classification. This suggests that most of the simulated mergers do not have conspicuous merger features and visually identified merger catalogues from observations are incomplete and biased towards certain merger types. The networks trained and tested with the same data perform the best, with observations performing better than simulations, a result of the observational sample being biased towards conspicuous mergers. Classifying SDSS observations with the simulation trained network has proven to work, providing tantalizing prospects for using simulation trained networks for galaxy identification in large surveys.Comment: Submitted to A&A, revised after first referee report. 20 pages, 22 figures, 14 tables, 1 appendi