La dernière décennie, la complexité des technologies embarqués a explosé et les flots de conception industrielle habituels ne suffisent plus pour proposer des produits fiables en respectant les exigences du marché. Ainsi, le développement de nouvelles méthodologies de conception est devenu un besoin impératif. La thèse vise l'amélioration des méthodologies de conception des systèmes embarqués. En proposant une approche de conception par niveaux d’abstraction, la nouvelle approche permet de guider et d’assister les concepteurs dans les étapes de conception, précisément de raffiner les composants de communication. Elle offre des garanties de préservation des propriétés fonctionnelles le long du flot de conception. La méthode proposée permet de raisonner sur les différents niveaux de description d'un système en exploitant des techniques de preuve de propriétés associées aux raffinement formel. / In the last decade, the complexity of embedded systems has exploded and the usual industrial design flows do not suffice any more to propose reliable products while respecting time to market constrain. Thus, developing new design methodologies has become an imperative. The thesis aims at the improvement of the methodologies of conception of the embedded systems. It proposes a method for assisting the process of refinement along the design flow. The proposed approach splits the design flow into multiple-levels, in order to guide the designer in the design process, from the most abstract model down to a synthesizable model. Furthermore, by using formal techniques the method allows to check the preservation of functional correctness along the design flow.

In this thesis are shown some results of realization of refinement monoid by Grothendieck monoids of von Neumann regular ring. The most important result of this thesis, recently published by P. Ara, J. Bosa and E. Pardo, claims that every finitely generated conical refinement monoid is realizable. We construct for each such monoid a von Neumann regular algebra such that monoid is realizable by this algebra. For this construction we use adaptable separated graphs and their relation to refinement monoids. 1

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18987号 / 工博第4029号 / 新制||工||1620(附属図書館) / 31938 / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 辻 伸泰, 教授 白井 泰治, 教授 松原 英一郎 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19708号 / 工博第4163号 / 新制||工||1642(附属図書館) / 32744 / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 辻 伸泰, 教授 白井 泰治, 教授 乾 晴行 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第20367号 / 工博第4304号 / 新制||工||1667(附属図書館) / 京都大学大学院工学研究科材料工学専攻 / (主査)教授 辻 伸泰, 教授 田中 功, 教授 乾 晴行 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

The development of adaptive mesh refinement capabilities in the field of computational fluid dynamics is an essential tool for enabling the simulation of larger and more complex physical problems. While such techniques have been known for a long time, most simulations do not make use of them because of the lack of a robust implementation. In this work, we present recent progresses that have been made to develop adaptive mesh refinement features in Nek5000, a code based on the spectral element method. These developments are driven by the algorithmic challenges posed by future exascale supercomputers. First, we perform the study of the strong scaling of Nek5000 on three petascale machines in order to assess the scalability of the code and identify the current bottlenecks. It is found that strong scaling limit ranges between 5, 000 and 220, 000 degrees of freedom per core depending on the machine and the case. The need for synchronized and low latency communication for efficient computational fluid dynamics simulation is also confirmed. Additionally, we present how Hypre, a library for linear algebra, is used to develop a new and efficient code for performing the setup step required prior to the use of an algebraic multigrid solver for preconditioning the pressure equation in Nek5000. Finally, the main objective of this work is to develop new methods for estimating the error on a numerical solution of the Navier–Stokes equations via the resolution of an adjoint problem. These new estimators are compared to existing ones, which are based on the decay of the spectral coefficients. Then, the estimators are combined with newly implemented capabilities in Nek5000 for automatic grid refinement and adaptive mesh adaptation is carried out. The applications considered so far are steady and two-dimensional, namely the lid-driven cavity at Re = 7, 500 and the flow past a cylinder at Re = 40. The use of adaptive mesh refinement techniques makes mesh generation easier and it is shown that a similar accuracy as with a static mesh can be reached with a significant reduction in the number of degrees of freedom. / <p>QC 20171114</p>

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Decision diagrams have recently emerged as a promising approach for difficult scheduling problems, along with other challenging discrete optimization problems. Decision diagrams can offer a compact representation of the solution space, and has the ability to capture complex constraints that are hard to model or express in other techniques. This thesis explores two standard construction methods for relaxed decision diagrams, top-down construction and incremental refinement. The techniques are compared on their ability to handle scheduling problems with multiple time windows and precedence constraints. The construction methods are evaluated on several metrics, including generated bound, execution time, and the size of the diagram, on instances of the problem with up to 200 tasks. The results show that incremental refinement generates smaller diagrams with good bounds when compared to the top-down compilation algorithm; the reduction in diagram size and increase in bounds for incremental refinement comes at the expense of execution time compared to top-down compilation.

In most finite element analysis, a uniform mesh is not the optimum way to model the problem. Mesh adaptation is the ability to modify a finite element model to include regions of the mesh with higher and lower node density. Mesh adaptation has received extensive study in both computational mechanics and computer graphics to increase the resolution or accuracy of the solution in specific areas. The algorithm developed in this thesis, the Automated Quadrilateral Coarsening by Ring Collapse (AQCRC) algorithm, provides a unique solution to allow conformal coarsening of both structured and unstructured quadrilateral finite element meshes. The algorithm is based on dual chord operations and dual chord removal. The AQCRC algorithm follows six steps: 1) input of a coarsening region and factor, 2) selection of coarsening rings, 3) improvement of mesh quality, 4) removal of coarsening rings, 5) mesh clean-up and 6) coarsening iterations. Examples are presented that show the application of the algorithm.

This thesis presents a new approach to conformal all-quadrilateral mesh adaptation. In finite element modeling applications, it is often desirable to modify the node density of the mesh; increasing the density in some parts of the mesh to provide more accurate results, while decreasing the density in other parts to reduce computation time. The desired node density is typically determined by a sizing function based on either the geometry of the model or the results of a finite element solution. Although there are numerous mesh adaptation methods currently in use, including initial adaptive mesh generation, node redistribution, and adaptive mesh refinement, there are relatively few methods that modify the mesh density by adding and removing mesh elements, and none of these guarantee a conformal, all-quadrilateral mesh while allowing general coarsening. This work introduces a new method that incorporates both conformal refinement and coarsening strategies on an existing mesh of any density or configuration. Given a sizing function, this method modifies the mesh by combining existing template based quadrilateral refinement methods with recent developments in localized quadrilateral coarsening and quality improvement into an automated mesh adaptation routine.