Parallel algorithms for nonlinear optimization

Parallel algorithm design is a very active research topic in optimization as parallel computer architectures have recently become easily accessible. This thesis is about an approach for designing parallel nonlinear programming algorithms. The main idea is to benefit from parallelization in designing new algorithms rather than considering direct parallelizations of the existing methods. We give a general framework following our approach, and then, give distinct algorithms that fit into this framework. The example algorithms we have designed either use procedures of existing methods within a multistart scheme, or they are completely new inherently parallel algorithms. In doing so, we try to show how it is possible to achieve parallelism in algorithm structure (at different levels) so that the resulting algorithms have a good solution performance in terms of robustness, quality of steps, and scalability. We complement our discussion with convergence proofs of the proposed algorithms

Productive and efficient computational science through domain-specific abstractions

In an ideal world, scientific applications are computationally efficient, maintainable and composable and allow scientists to work very productively. We argue that these goals are achievable for a specific application field by choosing suitable domain-specific abstractions that encapsulate domain knowledge with a high degree of expressiveness. This thesis demonstrates the design and composition of domain-specific abstractions by abstracting the stages a scientist goes through in formulating a problem of numerically solving a partial differential equation. Domain knowledge is used to transform this problem into a different, lower level representation and decompose it into parts which can be solved using existing tools. A system for the portable solution of partial differential equations using the finite element method on unstructured meshes is formulated, in which contributions from different scientific communities are composed to solve sophisticated problems. The concrete implementations of these domain-specific abstractions are Firedrake and PyOP2. Firedrake allows scientists to describe variational forms and discretisations for linear and non-linear finite element problems symbolically, in a notation very close to their mathematical models. PyOP2 abstracts the performance-portable parallel execution of local computations over the mesh on a range of hardware architectures, targeting multi-core CPUs, GPUs and accelerators. Thereby, a separation of concerns is achieved, in which Firedrake encapsulates domain knowledge about the finite element method separately from its efficient parallel execution in PyOP2, which in turn is completely agnostic to the higher abstraction layer. As a consequence of the composability of those abstractions, optimised implementations for different hardware architectures can be automatically generated without any changes to a single high-level source. Performance matches or exceeds what is realistically attainable by hand-written code. Firedrake and PyOP2 are combined to form a tool chain that is demonstrated to be competitive with or faster than available alternatives on a wide range of different finite element problems.Open Acces

Etude et simulations des phénomènes d'interactions satellite/plasma et de leurs impacts sur les mesures de plasmas basses énergies

Les satellites scientifiques sont immergés dans divers environnements spatiaux, entourés par des plasmas qu'ils sont supposés analyser, en utilisant des instruments de types détecteurs de particules. La présence de ces structures dans le plasma conduit à une variété d'interactions satellite/plasma complexes et inter-corrélées. L'environnement spatial influence la structure du satellite qui modifie son environnement. Les instruments embarqués mesurent un environnement perturbé et il est difficile de distinguer le signal naturel des mesures biaisées. Le but est d'étudier et d'améliorer la compréhension des interactions satellite/plasma, au moyen de simulations numériques effectuées avec le logiciel SPIS pour les basses énergies (<100 eV) puisque ces particules sont les plus affectées par les perturbations. L'objectif est de comprendre les mesures de plasmas sur des cas réalistes, en établissant une méthodologie de simulation de ces problématiques. Je simule les interactions ayant lieu entre les missions Solar Probe Plus, Solar Orbiter, Cluster dans leurs environnements respectifs et les mesures associées. L'analyse des résultats obtenus et leurs comparaisons à des données réelles permettent de comprendre les différents cas de figure et de valider la méthodologie développée au cours de cette thèse.Scientific satellites immersed in various space environments are surrounded by plasmas which they are supposed to analyze, using instruments such as particle detectors. The presence of these structures within the plasma leads to a variety of complex and inter-correlated spacecraft/plasma interactions. The space plasma modifies the satellite which in return disturbs its close environment. On-board instruments measure a perturbed plasma and it is difficult to distinguish the natural signal from biased measurements. The objective of this thesis is to study and improve the understanding of the spacecraft/plasma interactions, through numerical simulations performed with the SPIS software, on the low energy domain (<100 eV), as those particles are the most perturbed. The aim is to understand plasma measurements on realistic cases, by establishing a methodology of simulating those issues. I simulate interactions between the Solar Probe Plus, Solar Orbiter, Cluster missions and their respective environments, including the associated measurements. The analysis of the obtained results allows the understanding of the various cases and the validation of the methodology developed during this work