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We are interested in complex electronic structures of various atomic and ionics systems. We use an ab initioapproach, the multiconfigurational Dirac-Hartree-Fock (MCDHF), to compute atomic structures and properties.We contribute in three main ways to the already existent literature: by developing and implementing originalcomputer programs, by investigating possibilities of alternative computational methodologies and strategies, andfinally by performing accurate atomic structure calculations to support other research fields, i.e. nuclear physics,astrophysics or experimental physics, through the theoretical estimation of relevant atomic data.We raise questions about the choice of the optimal orbital basis by considering finite basis sets, MCDHF orbitalbases and natural-orbital bases. We demonstrate the promising potential of the latter in the context of hyperfinestructures and hope that others will find interest in pursuing our analysis. Ultimately, our work put forward someweaknesses of the traditional optimization strategy based on the layer-by-layer optimization strategy.We also perform large-scale calculations to determine accurate atomic properties such as energy levels, hyperfinestructures, isotope shifts, transition parameters, radiative lifetimes and Landé g factors. We show through thevariety of atomic properties and atomic systems studied, the difficulty of describing, in the relativistic framework,the correlation between the spatial position of electrons due to their Coulomb repulsion.This thesis is organized in two main parts. The first one is dedicated to the theoretical and computationalbackgrounds that are needed to understand the theoretical models and the interpretation of our results. Thesecond part presents and summarizes our articles and manuscripts. They are separated in four groups, A, B, C,and D, around the themes of the atomic orbital bases, the applications to nuclear physics, the applications toastrophysics, and investigations of negative ions. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

Šifrování multimediálních datových přenosů v reálném čase je jednou z úloh telekomunikační infrastruktury pro dosažení nezbytné úrovně zabezpečení. Rychlost provedení šifrovacího algoritmu může hrát klíčovou roli ve velikosti zpoždění jednotlivých paketů a proto je tento úkol zajímavým z hlediska optimalizačních metod. Tato práce se zaměřuje na možnosti paralelizace zpracování SRTP pro účely telefonní ústředny s využitím OpenCL frameworku a následnou analýzu potenciálního zlepšení.

Cette thèse propose une modélisation aussi générique que possible de la combustion dans les moteurs automobiles dans un cadre de simulation aux grandes échelles. Une première étude aborde la fermeture du terme de transport non résolu pour la flamme de prémélange. Par la suite, un couplage entre les modèles ecfm-les et pcm-fpi est proposé et validé pour intégrer les effets de chimie complexe à la simulation de la flamme de prémélange. Ce travail est étendu par l'adjonction de modélisations spécifiques à l'allumage par bougie et de l'auto-inflammation, toujours en intégrant les effets de chimie détaillée. Des calculs d'application aux combustions anormales dans les moteurs à allumage commandé concluent ce travail. / This work proposes a modeling as generic as possible of the combustion in automotive engines in the framework of large-eddy simulation. A first study addresses the closure of the non resolved transport term for the premixed flame. Then, a coupling between the models pcm-fpi and ecfm-les is proposed and validated to account for the detailed chemistry effects in the premixed flame modeling. This work is extended adding specific models for spark-ignition and auto-ignition, still integrating detailed chemistry effects. This work is ended by computations of abnormal combustions occurring in spark-ignition engines.

Nous proposons Dido, un langage dédié (DSL) implicitement parallèle qui capture les spécifications de haut niveau des stencils et génère automatiquement du code parallèle de haute performance pour les architectures à mémoire distribuée. Le code généré utilise ORWL en tant que interface de communication et runtime. Nous montrons que Dido réalise un grand progrès en termes de productivité sans sacrifier les performances. Dido prend en charge une large gamme de calculs stencils ainsi que des applications réelles à base de stencils. Nous montrons que le code généré par Dido est bien structuré et se prête à de différentes optimisations possibles. Nous combinons également la technique de génération de code de Dido avec Pluto l'optimiseur polyédrique de boucles pour améliorer la localité des données. Nous présentons des expériences qui prouvent l'efficacité et la scalabilité du code généré qui atteint de meilleures performances que les implémentations ORWL et MPI écrites à la main. / In this work, we present Dido, an implicitly parallel domain-specific language (DSL) that captures high-level stencil abstractions and automatically generates high-performance parallel stencil code for distributed-memory architectures. The generated code uses ORWL as a communication and synchronization backend. We show that Dido achieves a huge progress in terms of programmer productivity without sacrificing the performance. Dido supports a wide range of stencil computations and real-world stencil-based applications. We show that the well-structured code generated by Dido lends itself to different possible optimizations and study the performance of two of them. We also combine Dido's code generation technique with the polyhedral loop optimizer Pluto to increase data locality and improve intra-node data reuse. We present experiments that prove the efficiency and scalability of the generated code that outperforms both ORWL and MPI hand-crafted implementations.

Many partial differential equations (PDEs) admit conserved quantities like mass or energy. Those quantities are often essential to establish well-posed results. When approximating a PDE by a finite-difference scheme, it is natural to ask whether related discretized quantities remain conserved under the scheme. Such conservation may establish the stability of the numerical scheme. We present an algorithm for checking the preservation of a polynomial quantity under a polynomial finite-difference scheme. In our algorithm, schemes can be explicit or implicit, have higher-order time and space derivatives, and an arbitrary number of variables. Additionally, we present an algorithm for, given a scheme, finding conserved quantities. We illustrate our algorithm by studying several finite-difference schemes.

L'autonomie est l'une des préoccupations majeures lors du développement de missions spatiales que l'objectif soit scientifique (exploration interplanétaire, observations, etc) ou commercial (service en orbite). Pour le rendez-vous spatial, cette autonomie dépend de la capacité embarquée de contrôle du mouvement relatif entre deux véhicules spatiaux. Dans le contexte du service aux satellites (dépannage, remplissage additionnel d'ergols, correction d'orbite, désorbitation en fin de vie, etc), la faisabilité de telles missions est aussi fortement liée à la capacité des algorithmes de guidage et contrôle à prendre en compte l'ensemble des contraintes opérationnelles (par exemple, saturation des propulseurs ou restrictions sur le positionnement relatif entre les véhicules) tout en maximisant la durée de vie du véhicule (minimisation de la consommation d'ergols). La littérature montre que ce problème a été étudié intensément depuis le début des années 2000. Les algorithmes proposés ne sont pas tout à fait satisfaisants. Quelques approches, par exemple, dégradent les contraintes afin de pouvoir fonder l'algorithme de contrôle sur un problème d'optimisation efficace. D'autres méthodes, si elles prennent en compte l'ensemble du problème, se montrent trop lourdes pour être embarquées sur de véritables calculateurs existants dans les vaisseaux spatiaux. Le principal objectif de cette thèse est le développement de nouveaux algorithmes efficaces et validés pour le guidage et le contrôle impulsif des engins spatiaux dans le contexte des phases dites de "hovering" du rendez-vous orbital, i.e. les étapes dans lesquelles un vaisseau secondaire doit maintenir sa position à l'intérieur d'une zone délimitée de l'espace relativement à un autre vaisseau principal. La première contribution présentée dans ce manuscrit utilise une nouvelle formulation mathématique des contraintes d'espace pour le mouvement relatif entre vaisseaux spatiaux pour la conception d'algorithmes de contrôle ayant un traitement calculatoire plus efficace comparativement aux approches traditionnelles. La deuxième et principale contribution est une stratégie de contrôle prédictif qui assure la convergence des trajectoires relatives vers la zone de "hovering", même en présence de perturbations ou de saturation des actionneurs. [...] / Autonomy is one of the major concerns during the planning of a space mission, whether its objective is scientific (interplanetary exploration, observations, etc.) or commercial (service in orbit). For space rendezvous, this autonomy depends on the on-board capacity of controlling the relative movement between two spacecraft. In the context of satellite servicing (troubleshooting, propellant refueling, orbit correction, end-of-life deorbit, etc.), the feasibility of such missions is also strongly linked to the ability of the guidance and control algorithms to account for all operational constraints (for example, thruster saturation or restrictions on the relative positioning between the vehicles) while maximizing the life of the vehicle (minimizing propellant consumption). The literature shows that this problem has been intensively studied since the early 2000s. However, the proposed algorithms are not entirely satisfactory. Some approaches, for example, degrade the constraints in order to be able to base the control algorithm on an efficient optimization problem. Other methods accounting for the whole set of constraints of the problem are too cumbersome to be embedded on real computers existing in the spaceships. The main object of this thesis is the development of new efficient and validated algorithms for the impulsive guidance and control of spacecraft in the context of the so-called "hovering" phases of the orbital rendezvous, i.e. the stages in which a secondary vessel must maintain its position within a bounded area of space relatively to another main vessel. The first contribution presented in this manuscript uses a new mathematical formulation of the space constraints for the relative motion between spacecraft for the design of control algorithms with more efficient computational processing compared to traditional approaches. The second and main contribution is a predictive control strategy that has been formally demonstrated to ensure the convergence of relative trajectories towards the "hovering" zone, even in the presence of disturbances or saturation of the actuators.[...]

No description available.

In partial differential equations (PDEs), conserved quantities like mass and momentum are fundamental to understanding the behavior of the described physical systems. The preservation of conserved quantities is essential when using numerical schemes to approximate solutions of corresponding PDEs. If the discrete solutions obtained through these schemes fail to preserve the conserved quantities, they may be physically meaningless and unreliable. Previous approaches focused on checking conservation in PDEs and numerical schemes, but they did not give adequate attention to systematically handling parameters. This is a crucial aspect because many PDEs and numerical schemes have parameters that need to be dealt with systematically. Here, we investigate if the discrete analog of a conserved quantity is preserved under the solution induced by a parametric finite difference method. In this thesis, we modify and enhance a pre-existing algorithm to effectively and reliably deduce conserved quantities in the context of parametric schemes, using the concept of comprehensive Groebner systems. The main contribution of this work is the development of a versatile algorithm capable of handling various parametric explicit and implicit schemes, higher-order derivatives, and multiple spatial dimensions. The algorithm’s effectiveness and efficiency are demonstrated through examples and applications. In particular, we illustrate the process of selecting an appropriate numerical scheme among a family of potential discretization for a given PDE.

<p dir="ltr">Matrix decompositions play a pivotal role in matrix computation and applications. While general dense matrix-vector multiplications and linear equation solvers are prohibitively expensive, matrix decompositions offer fast alternatives for matrices meeting specific properties. This dissertation delves into my contributions to two fast matrix multiplication algorithms and one fast linear equation solver algorithm tailored for certain matrices and applications, all based on efficient matrix decompositions. Fast dimensionality reduction methods in spectral clustering, based on efficient eigen-decompositions, are also explored.</p><p dir="ltr">The first matrix decomposition introduced is the "kernel-independent" interpolative decomposition butterfly factorization (IDBF), acting as a data-sparse approximation for matrices adhering to a complementary low-rank property. Constructible in $O(N\log N)$ operations for an $N \times N$ matrix via hierarchical interpolative decompositions (IDs), the IDBF results in a product of $O(\log N)$ sparse matrices, each with $O(N)$ non-zero entries. This factorization facilitates rapid matrix-vector multiplication in $O(N \log N)$ operations, making it a versatile framework applicable to various scenarios like special function transformation, Fourier integral operators, and high-frequency wave computation.</p><p dir="ltr">The second matrix decomposition accelerates matrix-vector multiplication for computing multi-dimensional Jacobi polynomial transforms. Leveraging the observation that solutions to Jacobi's differential equation can be represented through non-oscillatory phase and amplitude functions, the corresponding matrix is expressed as the Hadamard product of a numerically low-rank matrix and a multi-dimensional discrete Fourier transform (DFT) matrix. This approach utilizes $r^d$ fast Fourier transforms (FFTs), where $r = O(\log n / \log \log n)$ and $d$ is the dimension, resulting in an almost optimal algorithm for computing the multidimensional Jacobi polynomial transform.</p><p dir="ltr">An efficient numerical method is developed based on a matrix decomposition, Hierarchical Interpolative Factorization, for solving modified Poisson-Boltzmann (MPB) equations. Addressing the computational bottleneck of evaluating Green's function in the MPB solver, the proposed method achieves linear scaling by combining selected inversion and hierarchical interpolative factorization. This innovation significantly reduces the computational cost associated with solving MPB equations, particularly in the evaluation of Green's function.</p><p dir="ltr"><br></p><p dir="ltr">Finally, eigen-decomposition methods, including the block Chebyshev-Davidson method and Orthogonalization-Free methods, are proposed for dimensionality reduction in spectral clustering. By leveraging well-known spectrum bounds of a Laplacian matrix, the Chebyshev-Davidson methods allow dimensionality reduction without the need for spectrum bounds estimation. And instead of the vanilla Chebyshev-Davidson method, it is better to use the block Chebyshev-Davidson method with an inner-outer restart technique to reduce total CPU time and a progressive polynomial filter to take advantage of suitable initial vectors when available, for example, in the streaming graph scenario. Theoretically, the Orthogonalization-Free method constructs a unitary isomorphic space to the eigenspace or a space weighting the eigenspace, solving optimization problems through Gradient Descent with Momentum Acceleration based on Conjugate Gradient and Line Search for optimal step sizes. Numerical results indicate that the eigenspace and the weighted eigenspace are equivalent in clustering performance, and scalable parallel versions of the block Chebyshev-Davidson method and OFM are developed to enhance efficiency in parallel computing.</p>