Time-dependent adjoint-based optimization of photonic crystals and metamaterials using a stabilized finite element method

In the current research, a time-dependent discrete adjoint algorithm for optimization of electromagnetic problems is developed. The proposed algorithm improves the efficiency for gradient-based optimization. The time-dependent Maxwell equations are discretized using a semi-discrete Petrov-Galerkin method, and time advancement is accomplished with an implicit, second-order backward differentiation formulation (BDF2). Utilizing the developed capability, two gradient-based shape design optimizations are conducted. In the first optimization an optical waveguide is designed with photonic crystals, and in the second an all-dielectric metamaterial is designed. A motivation for optimizing photonic crystals is due to their use as multi-band optical waveguides for telecommunication applications. For this design optimization, to ensure smooth surfaces, Bezier curves are employed to parametrically represent the shape. To reflect the design changes on the mesh, linear elasticity is used to adapt interior mesh points to boundary modifications. The cost function used in this design attempts to shift the band gap of the photonic crystals to desired frequency ranges. Results demonstrate a band gap shift from one single band gap to multiple band gaps is achievable. The motivation for optimizing broadband metamaterials is for their use as dielectric mirrors for applications where high power reflection is required. In this optimization, Hicks-Henne functions are utilized for shape parameterization and linear elasticity used once again for mesh adaptation. The cost function used attempts to widen the bandwidth of the metamaterial over a desired frequency range. Results demonstrate an increase of the full width at half maximum (FWHM) of reflection from 111THz to 303THz

Design optimization using CAD parameterization through CAPRI

Design optimization is one of the many areas of Computational Engineering that is directly applicable to almost any engineering endeavor. The design cycle is a multi-step process, beginning with a Computer Aided Design (CAD) model and ending with an optimized version of that model relative to some objective function. This is accomplished by parameterizing the model, through one of many different algorithms, and finding the ideal value of those parameters with respect to the specified objective. The purpose of this research is to explore the use of a Computational Analysis PRogramming Interface (CAPRI) for utilizing CAD parameters in design optimization along with exploring the steps taken to integrate this technology into a typical deterministic design optimization cycle. CAPRI is an interface developed by Robert Haimes of MIT which allows communication with CAD software during the various stages of computational design. A framework was developed for implementing CAPRI within the SimCenter\u27s current GEOMETRY libraries with the aim of improving geometry representation and accuracy. The framework also supports functionality to interface with a design optimization cycle by providing sensitivity derivatives and surface mesh coordinates throughout successive iterations. A sample wing was generated using SolidWorks as the CAD tool and the root and tip sections of a NACA 2412 airfoil. Design optimization was then performed upon this model with tip rotation and wing length as adjustable parameters

Dynamic response and maneuvering strategies of a hybrid autonomous underwater vehicle in hovering

Thesis (S.M. in Ocean Engineering)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Includes bibliographical references (p. 87-93).The Odyssey IV autonomous underwater vehicle (AUV) is the next generation of unmanned subsurface robots from the MIT Sea Grant AUV Laboratory. The Odyssey IV AUV has a novel propulsion system, which includes a pair of azimuthing thrusters for maneuvering in surge and heave. An analytical model was developed to describe the complex nonlinear vehicle dynamics, and experiments were performed to refine this model. The fluid dynamics of unsteady azimuthing marine propulsors are largely unstudied, especially for small vehicles like the Odyssey IV AUV. Experiments suggest that thrust developed by an azimuthing propulsor is dependent on the azimuth angle rate of change, and can substantially affect vehicle dynamics. A simple model capturing the effects of azimuthing on the thruster dynamics is developed, and is shown to improve behavior of the model.The use of azimuthing thrusters presents interesting problems and opportunities in maneuvering and control. Nonlinear model predictive control (MPC) is a technique that consists of the real-time optimization of a nonlinear dynamic system model, with the ability to handle constraints and nonlinearities. In this work, several variations of simulated and experimental MPC-based controllers are investigated. The primary challenge in applying nonlinear MPC to the Odyssey IV is solving the time intensive trajectory optimization problem online. Simulations suggest that MPC is able to capitalize on its knowledge of the system, allowing more aggressive trajectories than a traditional PID controller.by Lauren Alise Cooney.S.M.in Ocean Engineerin

Computational design, sensitivity analysis and optimization of fuel reforming catalytic reactor

In this research, the catalytic combustion of methane is numerically investigated using an unstructured, implicit, fully coupled finite volume approach. The nonlinear system of equations is solved by Newton’s method. The catalytic partial oxidation of methane over a rhodium catalyst in one channel of a coated honeycomb reactor is studied three-dimensionally, and eight gas-phase species (CH4, CO2, H2O, N2, O2, CO, OH and H2) are considered for the simulation. Surface chemistry is modeled by detailed reaction mechanisms including 38 heterogeneous reactions with 20 surface-adsorbed species for the Rh catalyst and 24 heterogeneous reactions with 11 surface-adsorbed species for Pt catalyst. The numerical results are compared with experimental data and good agreement is observed. Effects of the design variables, which include the inlet velocity, methane/oxygen ratio, catalytic wall temperature, and catalyst loading on the cost functions representing methane conversion and hydrogen production are numerically investigated. The sensitivity analysis for the reactor is performed using three different approaches: finite difference, direct differentiation and an adjoint method. Two gradient-based design optimization algorithms are utilized to improve the reactor performance. For additional test cases, the performance of two full scale honeycomb-structured reactors with 49 and 261 channels are investigated. The sensitivity analysis of the full reactor is performed using an adjoint method with four design variables consisting of the inlet velocity, inflow methane concentration, inlet oxygen density and thermal conductivity of the monolith

Controlling Hazardous Releases While Protecting Passengers in Civil Infrastructure Systems

The threat of accidental or deliberate toxic chemicals released into public spaces is a significant concern to public safety, and the real-time detection and mitigation of such hazardous contaminants has the potential to minimize harm and save lives. Furthermore, the safe evacuation of occupants during such a catastrophe is of utmost importance. This research entails a comprehensive means to address such scenarios, through both the sensing and control of contaminants, and the modeling of and potential communication to occupants as they evacuate. First, a computational fluid dynamics model has been developed that is capable of detecting and mitigating the hazardous contaminant over several time horizons using model predictive control optimization. Next, an evacuation agent-based model has been designed and coupled with the flow control model to simulate agents evacuating while interacting with a dynamic, threatening environment. Finally, a physical prototype (blower wind tunnel) has been constructed with capability of detection (via Ethernet-connected camera) of and mitigation (via compressed-air operated actuators) of a `contaminant' (i.e. smoke) to test the real-time feasibility of the computational fluid dynamics flow control model.PHDEnvironmental EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/135812/1/srimer_1.pd

Champ distance d'un solide paramétrique

RÉSUMÉ Ce mémoire présente une méthode novatrice de calcul du champ distance d'un solide paramétrique. Bien que de nombreux travaux aient déjà été préalablement réalisés sur le champ distance d'une géométrie polygonale, aucune solution n'avait encore été apportée pour obtenir celui d'une géométrie paramétrique. Le champ distance est un ensemble compact et fermé d'un espace euclidien, pour lequel est dénie en tout point la distance euclidienne minimale permettant de rejoindre la surface d'un solide. Le champ distance est calculé numériquement en résolvant une équation de transport basée sur l'équation Eikonal. L'équation Eikonal est une équation aux dérivées partielles du premier ordre, dites d'Hamilton-Jacobi. La résolution de l'équation Eikonal est un problème hyperbolique et non linéaire. Notre méthode repose sur le transport de conditions limites qui dépendent de la géométrie. L'information se propage le long des courbes caractéristiques à partir des conditions limites. Le caractère non linéaire du problème conduit à la formation de chocs, selon la loi de conservation hyperbolique. Nous avons utilisé une méthode de balayage, appelée Fast-Sweeping, pour résoudre l'équation Eikonal. Cette méthode consiste à discrétiser l'espace autour du solide à l'aide d'une grille cartésienne, puis à propager les conditions frontières en résolvant numériquement l'équation Eikonal selon un schéma de Godunov. La méthode de résolution peut être subdivisée en deux étapes. Dans un premier temps, il est nécessaire d'initialiser les conditions frontières. Dans un deuxième temps, l'équation Eikonal est résolue en utilisant plusieurs balayages alternés de Gauss-Seidel L'initialisation des conditions frontières est l'étape la plus importante et aussi la plus dicile à mettre en oeuvre lors du calcul du champ distance d'un solide. Les conditions limites sont constituées des noeuds limitrophes à la géométrie. Nous avons donc dû développer un algorithme permettant de détecter et d'initialiser précisément les noeuds frontières. Ces noeuds sont initialisés avec la valeur de la plus courte distance euclidienne permettant de rejoindre le solide. Cette distance minimale est obtenue en mesurant la longueur entre le noeud et sa projection sur la surface du solide.----------ABSTRACT In this thesis we propose a novel method for computing the distance field of parametric shapes. Although many works related to distance field of polygonal geometries have been published, no solution has still been brought to obtain the distance field of parametric geometries. Distance fields are defined as spatial fields of scalar distances to a surface geometry. At each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface. When the distance field is signed, we may also determine if the point is internal or external to objects within the domain. There is no closed form analytical formulas for computing the distance field of a manifold. Numerical methods are then necessary for computing the distance eld of such complex shapes. We use a front propagation method using the Eikonal equation to propagate the parametric surfaces. We use an iterative algorithm, called the Fast Sweeping method, for computing the numerical solution for Eikonal equation on a rectangular grid. The main idea of this method is to use a nonlinear Godunov upwind difference scheme to discretize the partial differental equation, and Gauss-Seidel iterations. Information propagates along characteristics from the boundary. Due to the nonlinearity of the propagation problem, characteristics may intersect like the formation of shocks in a hyperbolic conservation law. Boundary conditions are defined as the set of the closest grid nodes from the parametric surfaces. The initialisation of boundary conditions is the most difficult and the upmost critical step. Indeed we present a novel method for detecting boundary nodes on a rectangular grid using grid properties and projection criterias. We also present a new algorithm for the projection of points on rational Bezier surfaces using an euclidien distance optimisation

Méthodes sans factorisation pour l’optimisation non linéaire

RÉSUMÉ : Cette thèse a pour objectif de formuler mathématiquement, d'analyser et d'implémenter deux méthodes sans factorisation pour l'optimisation non linéaire. Dans les problèmes de grande taille, la jacobienne des contraintes n'est souvent pas disponible sous forme de matrice; seules son action et celle de sa transposée sur un vecteur le sont. L'optimisation sans factorisation consiste alors à utiliser des opérateurs linéaires abstraits représentant la jacobienne ou le hessien. De ce fait, seules les actions > sont autorisées et l'algèbre linéaire directe doit être remplacée par des méthodes itératives. Outre ces restrictions, une grande difficulté lors de l'introduction de méthodes sans factorisation dans des algorithmes d'optimisation concerne le contrôle de l'inexactitude de la résolution des systèmes linéaires. Il faut en effet s'assurer que la direction calculée est suffisamment précise pour garantir la convergence de l'algorithme concerné. En premier lieu, nous décrivons l'implémentation sans factorisation d'une méthode de lagrangien augmenté pouvant utiliser des approximations quasi-Newton des dérivées secondes. Nous montrons aussi que notre approche parvient à résoudre des problèmes d'optimisation de structure avec des milliers de variables et contraintes alors que les méthodes avec factorisation échouent. Afin d'obtenir une méthode possédant une convergence plus rapide, nous présentons ensuite un algorithme qui utilise un lagrangien augmenté proximal comme fonction de mérite et qui, asymptotiquement, se transforme en une méthode de programmation quadratique séquentielle stabilisée. L'utilisation d'approximations BFGS à mémoire limitée du hessien du lagrangien conduit à l'obtention de systèmes linéaires symétriques quasi-définis. Ceux-ci sont interprétés comme étant les conditions d'optimalité d'un problème aux moindres carrés linéaire, qui est résolu de manière inexacte par une méthode de Krylov. L'inexactitude de cette résolution est contrôlée par un critère d'arrêt facile à mettre en œuvre. Des tests numériques démontrent l'efficacité et la robustesse de notre méthode, qui se compare très favorablement à IPOPT, en particulier pour les problèmes dégénérés pour lesquels la LICQ n'est pas respectée à la solution ou lors de la minimisation. Finalement, l'écosystème de développement d'algorithmes d'optimisation en Python, baptisé NLP.py, est exposé. Cet environnement s'adresse aussi bien aux chercheurs en optimisation qu'aux étudiants désireux de découvrir ou d'approfondir l'optimisation. NLP.py donne accès à un ensemble de blocs constituant les éléments les plus importants des méthodes d'optimisation continue. Grâce à ceux-ci, le chercheur est en mesure d'implémenter son algorithme en se concentrant sur la logique de celui-ci plutôt que sur les subtilités techniques de son implémentation.----------ABSTRACT : This thesis focuses on the mathematical formulation, analysis and implementation of two factorization-free methods for nonlinear constrained optimization. In large-scale optimization, the Jacobian of the constraints may not be available in matrix form; only its action and that of its transpose on a vector are. Factorization-free optimization employs abstract linear operators representing the Jacobian or Hessian matrices. Therefore, only operator-vector products are allowed and direct linear algebra is replaced by iterative methods. Besides these implementation restrictions, a difficulty inherent to methods without factorization in optimization algorithms is the control of the inaccuracy in linear system solves. Indeed, we have to guarantee that the direction calculated is sufficiently accurate to ensure convergence. We first describe a factorization-free implementation of a classical augmented Lagrangian method that may use quasi-Newton second derivatives approximations. This method is applied to problems with thousands of variables and constraints coming from aircraft structural design optimization, for which methods based on factorizations fail. Results show that it is a viable approach for these problems. In order to obtain a method with a faster convergence rate, we present an algorithm that uses a proximal augmented Lagrangian as merit function and that asymptotically turns in a stabilized sequential quadratic programming method. The use of limited-memory BFGS approximations of the Hessian of the Lagrangian combined with regularization of the constraints leads to symmetric quasi-definite linear systems. Because such systems may be interpreted as the KKT conditions of linear least-squares problems, they can be efficiently solved using an appropriate Krylov method. Inaccuracy of their solutions is controlled by a stopping criterion which is easy to implement. Numerical tests demonstrate the effectiveness and robustness of our method, which compares very favorably with IPOPT, especially for degenerate problems for which LICQ is not satisfied at the optimal solution or during the minimization process. Finally, an ecosystem for optimization algorithm development in Python, code-named NLP.py, is exposed. This environment is aimed at researchers in optimization and students eager to discover or strengthen their knowledge in optimization. NLP.py provides access to a set of building blocks constituting the most important elements of continuous optimization methods. With these blocks, users are able to implement their own algorithm focusing on the logic of the algorithm rather than on the technicalities of its implementation