Ballistic (precessional) contribution to the conventional magnetic switching

We consider a magnetic moment with an easy axis anisotropy energy, switched by an external field applied along this axis. Additional small, time-independent bias field is applied perpendicular to the axis. It is found that the magnet's switching time is a non-monotonic function of the rate at which the field is swept from "up" to "down". Switching time exhibits a minimum at a particular optimal sweep time. This unusual behavior is explained by the admixture of a ballistic (precessional) rotation of the moment caused by the perpendicular bias field in the presence of a variable switching field. We derive analytic expressions for the optimal switching time, and for the entire dependence of the switching time on the field sweep time. The existence of the optimal field sweep time has important implications for the optimization of magnetic memory devices

Tiltrotor CFD part II: aerodynamic optimisation of tiltrotor blades

This paper presents aerodynamic optimisation of tiltrotor blades with high-fidelity computational fluid dynamics. The employed optimisation framework is based on a quasi-Newton method, and the required high-fidelity flow gradients were computed using a discrete adjoint solver. Single-point optimisations were first performed, to highlight the contrasting requirements of the helicopter and aeroplane flight regimes. It is then shown how a trade-off blade design can be obtained using a multi-point optimisation strategy. The parametrisation of the blade shape allowed to modify the twist and chord distributions, and to introduce a swept tip. The work shows how these main blade shape parameters influence the optimal performance of the tiltrotor in helicopter and aeroplane modes, and how a compromise blade shape can increase the overall tiltrotor performance. Moreover, in all the presented cases, the accuracy of the adjoint gradients resulted in a small number of flow evaluations for finding the optimal solution, thus indicating gradient-based optimisation as a viable tool for modern tiltrotor design

An Efficient Framework For Fast Computer Aided Design of Microwave Circuits Based on the Higher-Order 3D Finite-Element Method

In this paper, an efficient computational framework for the full-wave design by optimization of complex microwave passive devices, such as antennas, filters, and multiplexers, is described. The framework consists of a computational engine, a 3D object modeler, and a graphical user interface. The computational engine, which is based on a finite element method with curvilinear higher-order tetrahedral elements, is coupled with built-in or external gradient-based optimization procedures. For speed, a model order reduction technique is used and the gradient computation is achieved by perturbation with geometry deformation, processed on the level of the individual mesh nodes. To maximize performance, the framework is targeted to multicore CPU architectures and its extended version can also use multiple GPUs. To illustrate the accuracy and high efficiency of the framework, we provide examples of simulations of a dielectric resonator antenna and full-wave design by optimization of two diplexers involving tens of unknowns, and show that the design can be completed within the duration of a few simulations using industry-standard FEM solvers. The accuracy of the design is confirmed by measurements

Optimal design application on the advanced aeroelastic rotor blade

The vibration and performance optimization procedure using regression analysis was successfully applied to an advanced aeroelastic blade design study. The major advantage of this regression technique is that multiple optimizations can be performed to evaluate the effects of various objective functions and constraint functions. The data bases obtained from the rotorcraft flight simulation program C81 and Myklestad mode shape program are analytically determined as a function of each design variable. This approach has been verified for various blade radial ballast weight locations and blade planforms. This method can also be utilized to ascertain the effect of a particular cost function which is composed of several objective functions with different weighting factors for various mission requirements without any additional effort

A rational deferred correction approach to parabolic optimal control problems

The accurate and efficient solution of time-dependent PDE-constrained optimization problems is a challenging task, in large part due to the very high dimension of the matrix systems that need to be solved. We devise a new deferred correction method for coupled systems of time-dependent PDEs, allowing one to iteratively improve the accuracy of low-order time stepping schemes. We consider two variants of our method, a splitting and a coupling version, and analyze their convergence properties. We then test our approach on a number of PDE-constrained optimization problems. We obtain solution accuracies far superior to that achieved when solving a single discretized problem, in particular in cases where the accuracy is limited by the time discretization. Our approach allows for the direct reuse of existing solvers for the resulting matrix systems, as well as state-of-the-art preconditioning strategies

Lunar Ascent and Orbit Injection via Neighboring Optimal Guidance and Constrained Attitude Control

Future human or robotic missions to the Moon will require efficient ascent path and accurate orbit injection maneuvers, because the dynamical conditions at injection affect the subsequent phases of spaceflight. This research focuses on the original combination of two techniques applied to lunar ascent modules, i.e., (1) the recently introduced variable-time-domain neighboring optimal guidance (VTD-NOG), and (2) a constrained proportional-derivative (CPD) attitude control algorithm. VTD-NOG belongs to the class of feedback implicit guidance approaches aimed at finding the corrective control actions capable of maintaining the spacecraft sufficiently close to the reference trajectory. CPD pursues the desired attitude using thrust vector control while constraining the rate of the thrust deflection angle. The numerical results unequivocally demonstrate that the joint use of VTD-NOG and CPD represents an accurate and effective methodology for guidance and control of lunar ascent path and orbit injection in the presence of nonnominal flight conditions

TMB: Automatic Differentiation and Laplace Approximation

TMB is an open source R package that enables quick implementation of complex nonlinear random effect (latent variable) models in a manner similar to the established AD Model Builder package (ADMB, admb-project.org). In addition, it offers easy access to parallel computations. The user defines the joint likelihood for the data and the random effects as a C++ template function, while all the other operations are done in R; e.g., reading in the data. The package evaluates and maximizes the Laplace approximation of the marginal likelihood where the random effects are automatically integrated out. This approximation, and its derivatives, are obtained using automatic differentiation (up to order three) of the joint likelihood. The computations are designed to be fast for problems with many random effects (~10^6) and parameters (~10^3). Computation times using ADMB and TMB are compared on a suite of examples ranging from simple models to large spatial models where the random effects are a Gaussian random field. Speedups ranging from 1.5 to about 100 are obtained with increasing gains for large problems. The package and examples are available at http://tmb-project.org