Scalable electronic structure methods to solve the Kohn-Sham equation

From the single hydrogen to proteins in the hundreds of thousands of kilodaltons, scientists can use the electronic structure of interacting atoms to predict their material properties. Knowing the material properties through solving the electronic structure problem, would allow for the controlled prediction and corresponding design of materials. The Kohn-Sham equations, based on density functional theory, transform a many-body problem impossible to solve for anything but the smallest molecules, into a practical problem which can be used to predict material properties. Although KSDFT scales as the cube of the number of electrons in the system, there are additional well documented approximations to further reduce the number of electrons, such as the pseudopotential method. The incoming exascale era will lead to unavoidable challenges in solving the Kohn-Sham equations. These challenges include communication and hardware considerations. Old paradigms, epitomized by repeated series of globally forced synchronization points, will give way to new breeds of algorithms to maximizing scaling performance while maintaining portability. This thesis focuses on the solution to Kohn-Sham DFT in real space at scale. Key to this effort is a parallel treatment of numerical elements involving the Rayleigh-Ritz method. At minimum, the Rayleigh-Ritz projection requires a number of distributed matrix vector operations equal to the number of electrons solved for in a system. Furthermore, the projection requires that number, squared and then halved, of dot products. The memory cost for such an algorithm also grows very large quickly, and explicit intelligent management is not an option. I demonstrate the computational requirements for the various steps in solving for the electronic structure problem for both large and small molecular systems. This thesis also discusses opportunities in real space Kohn-Sham DFT to further utilize floating point optimized hardware the with higher order stencils.Chemical Engineerin

Prediction of the vibroacoustic response of aerospace composite structures in a broadband frequency range

Pendant sa mission, un lanceur est soumis à des excitations large bande, sévères, aérodynamiques, de provenances diverses, qui peuvent mettre en danger la survivabilité de la charge utile et de l équipement électronique du véhicule, et par conséquent le succès de la mission. Les structures aérospatiales sont généralement caractérisées par l utilisation de matériaux composites exotiques des configurations et des épaisseurs variantes, ainsi que par leurs géométries largement complexes. Il est donc d une importance cruciale pour l industrie aérospatiale moderne, le développement d outils analytiques et numériques qui peuvent prédire avec précision la réponse vibroacoustique des structures larges, composites de différentes géométries et soumis à une combinaison des excitations aéroacoustiques. Récemment, un grand nombre de recherches ont été menées sur la modélisation des caractéristiques de propagation des ondes au sein des structures composites. Dans cette étude, la méthode des éléments finis ondulatoires (WFEM) est utilisée afin de prédire les caractéristiques de dispersion des ondes dans des structures composites orthotropes de géométries variables, nommément des plaques plates, des panneaux simplement courbés, des panneaux doublement courbés et des coques cylindriques. Ces caractéristiques sont initialement utilisées pour prédire la densité modale et le facteur de perte par couplage des structures connectées au milieu acoustique. Par la suite, la perte de transmission (TL) à large bande des structures modélisées dans le cadre d une analyse statistique énergétique (SEA) dans un contexte ondulatoire est calculée. Principalement en raison de la complexité géométrique importante de structures, l utilisation des éléments finis (FE) au sein de l industrie aérospatiale est souvent inévitable. L utilisation de ces modèles est limitée principalement à cause du temps de calcul exigé, même pour les calculs dans la bande basses fréquences. Au cours des dernières années, beaucoup de chercheurs travaillent sur la réduction de modèles FE, afin de rendre leur application possible pour des systèmes larges. Dans cette étude, l approche de SOAR est adoptée, afin de minimiser le temps de calcul pour un système couplé de type structurel-acoustique, tout en conservant une précision satisfaisante de la prédiction dans un sens large bande. Le système est modélisé sous diverses excitations aéroacoustiques, nommément un champ acoustique diffus et une couche limite turbulente (TBL).La validation expérimentale des outils développés est réalisée sur un ensemble de structures sandwich composites orthotropes. Ces derniers sont utilisés afin de formuler une approche couche équivalente unique (ESL) pour la modélisation de la réponse spatiale du panneau dans le contexte d une approche de matrice de raideur dynamique. L effet de la température de la structure ainsi que du milieu acoustique sur la réponse du système vibroacoustique est examiné et analysé. Par la suite, un modèle de la structure SYLDA, également fait d un matériau sandwich orthotrope, est testé principalement dans le but d enquêter sur la nature de couplage entre ses divers sous-systèmes. La modélisation ESL précédemment développée est utilisé pour un calcul efficace de la réponse de la structure dans la gamme des basses et moyennes fréquences, tandis que pour des fréquences plus élevées, une hybridisation WFEM / FEM pour la modélisation des structures discontinues est utilisé.During its mission, a launch vehicle is subject to broadband, severe, aeroacoustic and structure-borne excitations of various provenances, which can endanger the survivability of the payload and the vehicles electronic equipment, and consequently the success of the mission. Aerospace structures are generally characterized by the use of exotic composite materials of various configurations and thicknesses, as well as by their extensively complex geometries and connections between different subsystems. It is therefore of crucial importance for the modern aerospace industry, the development of analytical and numerical tools that can accurately predict the vibroacoustic response of large, composite structures of various geometries and subject to a combination of aeroacoustic excitations. Recently, a lot of research has been conducted on the modelling of wave propagation characteristics within composite structures. In this study, the Wave Finite Element Method (WFEM) is used in order to predict the wave dispersion characteristics within orthotropic composite structures of various geometries, namely flat panels, singly curved panels, doubly curved panels and cylindrical shells. These characteristics are initially used for predicting the modal density and the coupling loss factor of the structures connected to the acoustic medium. Subsequently the broad-band Transmission Loss (TL) of the modelled structures within a Statistical Energy Analysis (SEA) wave-context approach is calculated. Mainly due to the extensive geometric complexity of structures, the use of Finite Element(FE) modelling within the aerospace industry is frequently inevitable. The use of such models is limited mainly because of the large computation time demanded even for calculations in the low frequency range. During the last years, a lot of researchers focus on the model reduction of large FE models, in order to make their application feasible. In this study, the Second Order ARnoldi (SOAR) reduction approach is adopted, in order to minimize the computation time for a fully coupled composite structural-acoustic system, while at the same time retaining a satisfactory accuracy of the prediction in a broadband sense. The system is modelled under various aeroacoustic excitations, namely a diffused acoustic field and a Turbulent Boundary Layer (TBL) excitation. Experimental validation of the developed tools is conducted on a set of orthotropic sandwich composite structures. Initially, the wave propagation characteristics of a flat panel are measured and the experimental results are compared to the WFEM predictions. The later are used in order to formulate an Equivalent Single Layer (ESL) approach for the modelling of the spatial response of the panel within a dynamic stiffness matrix approach. The effect of the temperature of the structure as well as of the acoustic medium on the vibroacoustic response of the system is examined and analyzed. Subsequently, a model of the SYLDA structure, also made of an orthotropic sandwich material, is tested mainly in order to investigate the coupling nature between its various subsystems. The developed ESL modelling is used for an efficient calculation of the response of the structure in the lower frequency range, while for higher frequencies a hybrid WFEM/FEM formulation for modelling discontinuous structures is used.LYON-Ecole Centrale (690812301) / SudocSudocFranceF

Graph Inference with Applications to Low-Resource Audio Search and Indexing

The task of query-by-example search is to retrieve, from among a collection of data, the observations most similar to a given query. A common approach to this problem is based on viewing the data as vertices in a graph in which edge weights reflect similarities between observations. Errors arise in this graph-based framework both from errors in measuring these similarities and from approximations required for fast retrieval. In this thesis, we use tools from graph inference to analyze and control the sources of these errors. We establish novel theoretical results related to representation learning and to vertex nomination, and use these results to control the effects of model misspecification, noisy similarity measurement and approximation error on search accuracy. We present a state-of-the-art system for query-by-example audio search in the context of low-resource speech recognition, which also serves as an illustrative example and testbed for applying our theoretical results

Finite elements software and applications

The contents of this thesis are a detailed study of the software for the finite element method. In the text, the finite element method is introduced from both the engineering and mathematical points of view. The computer implementation of the method is explained with samples of mainframe, mini- and micro-computer implementations. A solution is presented for the problem of limited stack size for both mini- and micro-computers which possess stack architecture. Several finite element programs are presented. Special purpose programs to solve problems in structural analysis and groundwater flow are discussed. However, an efficient easy-to-use finite element program for general two-dimensional problems is presented. Several problems in groundwater flow are considered that include steady, unsteady flows in different types of aquifers. Different cases of sinks and sources in the flow domain are also considered. The performance of finite element methods is studied for the chosen problems by comparing the numerical solutions of test problems with analytical solutions (if they exist) or with solutions obtained by other numerical methods. The polynomial refinement of the finite elements is studied for the presented problems in order to offer some evidence as to which finite element simulation is best to use under a variety of circumstances

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Electronic transport in nanoelectromechanical systems : noise, back-action, and quantum measurement

The important progress made in nanolitography processes in the last decades has had a profound impact in our daily lives, by making possible the miniaturization of consumer electronics. Unbeknownst to most consumers, it is nowadays possible to fabricate free-standing nanoscale devices, that will naturally vibrate under thermal or external excitation. Over the last decade, a new subfield of physics devoted to studying these objects emerged: nanomechanics. In this thesis, we study electronic transport in such nanostructures where mechanical degrees of freedom play an important role. More precisely, we calculate the full transport properties (e.g. average current, frequency-dependent current noise) of different mesoscopic detectors in the presence of coupling to a nanomechanical oscillator. The objective of our study is twofold. First, there is a strong interest in understanding the effect that the coupling to electronic degrees of freedom has on the state of the mechanical system. We will show that under many conditions the interaction with the detector can be understood in terms of an effective thermal bath, but also discuss the limitations of this effective environment model. A second main aspect of the work presented here is the calculation of the signature of the mechanical object in the transport properties of the detector. As one of the primary goal in the field of nanoelectromechanical systems is to use the output of such electrical detectors to achieve position measurements at the quantum limit, this question obviously is of great relevance to the field. This thesis is organized in 3 main parts, each associated with a different electronic detector. After a short introduction to nanoelectromechanical systems, we focus in Part II on a system composed a single-electron transistor coupled capacitively to a classical mechanical oscillator. We present a complete study of the transport properties of the coupled system, going beyond the usual weak-coupling approximation. In Part III, we discuss the properties of a system where a tunnel junction is coupled to the mechanical object. Looking at this system from the point of view of quantum measurement, we analyze the transport properties of a system composed of two independent tunnel junctions coupled to the same oscillator and demonstrate how, by using the cross correlated output of the two detectors, one can improve the sensitivity of position measurements beyond the usual quantum limit. In this part, we also demonstrate that the current noise of a system composed of two tunnel junctions (one with fixed transmission amplitude, the other with position-dependent transmission amplitude) can contain information about the momentum of the mechanical oscillator. Lastly, in Part IV we study a system composed of a mechanical oscillator coupled to a superconducting single-electron transistor. The coupled dynamics of the oscillator and mesoscopic detector are in this case very complex, and we demonstrate how a numerical approach based on a solution of the Liouville equation can be used to validate results obtained from approximate analytical approaches. We also demonstrate, by looking at the frequency-dependence of the charge fluctuations on the superconducting single-electron transistor, limitations to the model where the effect of the detector back-action on the oscillator is modeled as an effective environment