A Parallel Iterative Method for Computing Molecular Absorption Spectra

We describe a fast parallel iterative method for computing molecular absorption spectra within TDDFT linear response and using the LCAO method. We use a local basis of "dominant products" to parametrize the space of orbital products that occur in the LCAO approach. In this basis, the dynamical polarizability is computed iteratively within an appropriate Krylov subspace. The iterative procedure uses a a matrix-free GMRES method to determine the (interacting) density response. The resulting code is about one order of magnitude faster than our previous full-matrix method. This acceleration makes the speed of our TDDFT code comparable with codes based on Casida's equation. The implementation of our method uses hybrid MPI and OpenMP parallelization in which load balancing and memory access are optimized. To validate our approach and to establish benchmarks, we compute spectra of large molecules on various types of parallel machines. The methods developed here are fairly general and we believe they will find useful applications in molecular physics/chemistry, even for problems that are beyond TDDFT, such as organic semiconductors, particularly in photovoltaics.Comment: 20 pages, 17 figures, 3 table

On the parallel scalability of hybrid linear solvers for large 3D problems

Large-scale scientific applications and industrial simulations are nowadays fully integrated in many engineering areas. They involve the solution of large sparse linear systems. The use of large high performance computers is mandatory to solve these problems. The main topic of this research work was the study of a numerical technique that had attractive features for an efficient solution of large scale linear systems on large massively parallel platforms. The goal is to develop a high performance hybrid direct/iterative approach for solving large 3D problems. We focus specifically on the associated domain decomposition techniques for the parallel solution of large linear systems. We have investigated several algebraic preconditioning techniques, discussed their numerical behaviours, their parallel implementations and scalabilities. We have compared their performances on a set of 3D grand challenge problems

Electrohydrodynamic instabilities in freely suspended viscous films under normal electric fields

Electrohydrodynamic instabilities of fluid-fluid interfaces can be exploited in various microfluidic applications in order to enhance mixing, replicate well-controlled patterns or generate drops of a particular size. In this work, we study the stability and dynamics of a system of three superimposed layers of two immiscible fluids subject to a normal electric field. Following the Taylor-Melcher leaky dielectric model, the bulk remains electroneutral while a net charge accumulates on the interfaces. The interfacial charge dynamics is captured by a conservation equation accounting for Ohmic conduction, advection by the flow and finite charge relaxation. Using this model, we perform a linear stability analysis and identify different modes of instability, and we characterize the behavior of the system as a function of the relevant dimensionless groups in each mode. Further, we perform numerical simulations using the boundary element method in order to study the effect of nonlinearities on long-time interfacial dynamics. We demonstrate how the coupling of flow and surface charge transport in different modes of instability can give rise to nonlinear phenomena such as tip streaming or pinching of the film into droplets

Metric-based anisotropic mesh adaptation for 3D acoustic boundary element methods

International audienceThis paper details the extension of a metric-based anisotropic mesh adaptation strategy to the boundary element method for problems of 3D acoustic wave propagation. Traditional mesh adaptation strategies for boundary element methods rely on Galerkin discretizations of the boundary integral equations, and the development of appropriate error indicators. They often require the solution of further integral equations. These methods utilise the error indicators to mark elements where the error is above a specified tolerance and then refine these elements. Such an approach cannot lead to anisotropic adaptation regardless of how these elements are refined, since the orientation and shape of current elements cannot be modified. In contrast, the method proposed here is independent of the discretization technique (e.g., collocation, Galerkin). Furthermore, it completely remeshes at each refinement step, altering the shape, size, and orientation of each element according to an optimal metric based on a numerically recovered Hessian of the boundary solution. The resulting adaptation procedure is truly anisotropic and independent of the complexity of the geometry. We show via a variety of numerical examples that it recovers optimal convergence rates for domains with geometric singularities. In particular, a faster convergence rate is recovered for scattering problems with complex geometries

A perturbed two-level preconditioner for the solution of three-dimensional heterogeneous Helmholtz problems with applications to geophysics

Le sujet de cette thèse est le développement de méthodes itératives permettant la résolution de grands systèmes linéaires creux d'équations présentant plusieurs seconds membres simultanément. Ces méthodes seront en particulier utilisées dans le cadre d'une application géophysique : la migration sismique visant à simuler la propagation d'ondes sous la surface de la terre. Le problème prend la forme d'une équation d'Helmholtz dans le domaine fréquentiel en trois dimensions, discrétisée par des différences finies et donnant lieu à un système linéaire creux, complexe, non-symétrique, non-hermitien. De plus, lorsque de grands nombres d'onde sont considérés, cette matrice possède une taille élevée et est indéfinie. Du fait de ces propriétés, nous nous proposons d'étudier des méthodes de Krylov préconditionnées par des techniques hiérarchiques deux niveaux. Un tel pre-conditionnement s'est montré particulièrement efficace en deux dimensions et le but de cette thèse est de relever le défi de l'adapter au cas tridimensionel. Pour ce faire, des méthodes de Krylov sont utilisées à la fois comme lisseur et comme méthode de résolution du problème grossier. Ces derniers choix induisent l'emploi de méthodes de Krylov dites flexibles. ABSTRACT : The topic of this PhD thesis is the development of iterative methods for the solution of large sparse linear systems of equations with possibly multiple right-hand sides given at once. These methods will be used for a specific application in geophysics - seismic migration - related to the simulation of wave propagation in the subsurface of the Earth. Here the three-dimensional Helmholtz equation written in the frequency domain is considered. The finite difference discretization of the Helmholtz equation with the Perfect Matched Layer formulation produces, when high frequencies are considered, a complex linear system which is large, non-symmetric, non-Hermitian, indefinite and sparse. Thus we propose to study preconditioned flexible Krylov subspace methods, especially minimum residual norm methods, to solve this class of problems. As a preconditioner we consider multi-level techniques and especially focus on a two-level method. This twolevel preconditioner has shown efficient for two-dimensional applications and the purpose of this thesis is to extend this to the challenging three-dimensional case. This leads us to propose and analyze a perturbed two-level preconditioner for a flexible Krylov subspace method, where Krylov methods are used both as smoother and as approximate coarse grid solver

Large Eddy Simulation of Vertical AxisWind Turbine for Low Reynolds Number Applications

Research of low to intermediate Reynolds numbers flows (1000 < Re < 1000000) has become essential in the last two decades due to increasing interest in small Unmanned Aerial Vehicles (UAVs), small wind turbines, and exploration of planets such as Mars. Simulation of many of these applications need an accurate prediction of aerodynamic forces within five percent accuracy. Therefore, developing high accurate Computational Fluid Dynamics (CFD) tools is essential to design and optimize these systems. Simulation of a Vertical Axis Wind Turbine (VAWT) on Mars is considered as the motivating application in this project. It is motivated by current plans of sending humans to Mars in the next two decades, and the need to investigate sustainable way to generate power on the planet. VAWTs have a simple geometry but the flow structure around the blade is known to be one of the most complex flow in aerodynamics. Separation, vortex shedding and dynamic stall frequently occurs on the turbines’ blade. Therefore a tool that accurately simulates the flow around wind turbines, accurately, is needed. Large eddy simulation has proven to be a reliable turbulence model with the capability of simulation flows with regions of separation and transition to turbulence. Growth of the computational capability along with development of more accurate numerical methods and new advanced LES models has permitted the use of wall-resolved LES. In the current dissertation, Wall-Adapting Local Eddy-Viscosity (WALE) simulation is used to simulate flow around a vertical axis wind turbine. Using a second-order accurate discretization technique, both in space and time, with a low-dissipative method, enforced by an adjustable upwinding factor, achieves the required accuracy in Large Eddy Simulation. The proposed approach enables us to accurately predict the shear stress and pressure distribution on the blade. Therefore, dynamic stall location is spotted precisely. The potential to increase the performance of small VAWTs by using Morphing blades are very promising. An in-house code has been extended to simulation flow around dynamically morphing blades. Therefore, Arbitrary Lagrangian Eulerian (ALE) is used to preserve the second order accuracy of the numerical scheme under a dynamic mesh, and a combination of spring and diffusion methods is used to adjust the mesh dynamically around deforming blades. A morphing blade scenario is presented to show the new capability developed

Plasmons in nanoparticles: atomistic Ab Initio theory for large systems

205 p.El trabajo realizado en esta tesis doctoral se centra en la implementación de nuevos algoritmos y de suaplicación en diferentes tipos de nanoestructuras. El programa científico en el que se han llevado a cabolas extensiones es una implementación eficiente de la teoría funcional de densidad dependiente deltiempo, conocida como MBPT-LCAO.Las principales extensiones realizadas son las siguientes: implementación de la espectroscopía de pérdidade energía de electrones en el espacio real, mejora del procedimiento iterativo para permitir cálculos degran tamaño sin precedentes, cálculo del campo eléctrico inducido e implementación de la espectroscopíade dispersión Raman.Estas implementaciones se han utilizado en agregados y agregados dímeros de sodio y plata, así como ennanotubos de carbono y nitruro de boro. Se han calculado tanto el espectro de absorción como los camposeléctricos inducidos para todos estos sistemas. De esta forma, este trabajo nos ha permitido entendermejor la respuesta de tales nanoestructuras bajo la influencia de una perturbación externa

Schémas cinétiques réduits et couplage thermique pour les simulations aux grandes échelles du cliquetis dans les moteurs à piston

Pour améliorer le rendement des moteurs essence, une méthode efficace est le downsizing qui consiste en la diminution de la cylindrée moteur compensée par l’ajout d’un compresseur pour maintenir la puissance. Lorsque le niveau de downsizing est trop important les fortes pression et températures rencontrées favorisent l’apparition de phénomènes d’auto-allumage de type cliquetis ou rumble néfastes pour l’intégrité du moteur. Ce type de phénomène, aujourd’hui encore mal compris, constitue une limite à l’utilisation du downsizing. Dans cette thèse la Simulation aux Grandes Echelles est utilisée pour étudier ce type de combustion dite anormale. L’objectif est de proposer une méthodologie numérique capable de reproduire leurs apparitions pour en étudier les mécanismes. L’auto-allumage est un mode de combustion sensible aux variations des conditions thermodynamiques locales. Des méthodes numériques précises et des modèles appropriés, en particulier pour la thermique paroi doivent donc être utilisés. La première partie de ce manuscrit présente la méthodologie numérique proposée et en particulier deux aspects développés lors de cette thèse: un modèle d’auto-allumage qui permet de reproduire le délai d’auto-allumage des gaz frais avec un schéma cinétique réduit et une méthodologie de couplage entre la chambre de combustion et la culasse permettant de définir des champs de températures paroi réalistes. La seconde partie de ce manuscrit présente les résultats de deux études numériques reproduisant certains points de fonctionnement d’un moteur expérimental. La première étude est réalisée à l’aide de modèles de combustion de la littérature et vise à reproduire le comportement expérimental pour diverses variations paramétriques influant sur la combustion. La seconde étude est réalisée à l’aide des modèles développés dans cette thèse afin d’étudier l’impact de la thermique paroi dans les mécanismes d’apparition des combustions anormales

Plasmons in nanoparticles: atomistic Ab Initio theory for large systems

205 p.El trabajo realizado en esta tesis doctoral se centra en la implementación de nuevos algoritmos y de suaplicación en diferentes tipos de nanoestructuras. El programa científico en el que se han llevado a cabolas extensiones es una implementación eficiente de la teoría funcional de densidad dependiente deltiempo, conocida como MBPT-LCAO.Las principales extensiones realizadas son las siguientes: implementación de la espectroscopía de pérdidade energía de electrones en el espacio real, mejora del procedimiento iterativo para permitir cálculos degran tamaño sin precedentes, cálculo del campo eléctrico inducido e implementación de la espectroscopíade dispersión Raman.Estas implementaciones se han utilizado en agregados y agregados dímeros de sodio y plata, así como ennanotubos de carbono y nitruro de boro. Se han calculado tanto el espectro de absorción como los camposeléctricos inducidos para todos estos sistemas. De esta forma, este trabajo nos ha permitido entendermejor la respuesta de tales nanoestructuras bajo la influencia de una perturbación externa