The New Macroeconometrics may succinctly be described as the application of Bayesian analysis to the class of macroeconomic models called Dynamic Stochastic General Equilibrium (DSGE) models. A prominent local example from this research area is the development and estimation of the RAMSES model, the main macroeconomic model in use at Sveriges Riksbank.   Bayesian estimation of DSGE models is often computationally demanding. In this thesis fast algorithms for Bayesian inference are developed and tested in the context of the state space model framework implied by DSGE models. The algorithms discussed in the thesis deal with evaluation of the DSGE model likelihood function and sampling from the posterior distribution. Block Kalman filter algorithms are suggested for likelihood evaluation in large linearised DSGE models. Parallel particle filter algorithms are presented for likelihood evaluation in nonlinearly approximated DSGE models. Prefetching random walk Metropolis algorithms and adaptive hybrid sampling algorithms are suggested for posterior sampling. The generality of the algorithms, however, suggest that they should be of interest also outside the realm of macroeconometrics.

With over 830,000 km of operating pipeline in Canada alone, their safe and continued functioning underpins much of daily life. A key type of risk associated with pipelines is third-party damage, damage caused by actions not associated with the pipelines normal operation. The question of whether the pressurized structure like pipeline or pressure vessel would undergo “unzipping” due to the third-party impact is crucial for the safety of pipelines or pressure vessels in service needs to be answered. Thus, we endeavour to develop a methodology for assessment of design solutions effectiveness to prevent a pipeline or pressure vessel failure in an abrupt explosion-like fashion due to third-party damage. Model of crack propagation determining whether the “unzipping” rupture will occur is viewed as a key element in the safety-driven design procedure providing significant effect on the safety of operation. The crack propagation modeling is achieved through the use of nonlinear fracture mechanics technique. The method of singular integral equations is used to calculate the critical stress required for the catastrophic failure of pipeline or pressure vessel damaged due to third-party interference. The model was implemented as a FORTRAN program. Testing of the developed numerical tool was performed using experimental data available in the literature, with the results showing promising agreement. / February 2016

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Dans le domaine du calcul de haute performance, les architectures d’exécution sont en continuelle évolution. L’augmentation du nombre de nœuds de calcul, ou le choix d’une topologie réseau plus rapide représentent un investissement important tant en temps qu’en moyen financier. Les méthodes de prédiction de performances permettent de guider ce choix. En parallèle à ce développement, les systèmes HPC pair-à-pair (P2P) se sont également développés ces dernières années. Ce type d’architecture hétérogène permettrait la résolution des problèmes scientifiques pour un coût très faible par rapport au coût d’une architecture dédiée.Ce manuscrit présente une méthode nouvelle de prédiction de performances pour les applications réelles de calcul distribué, exécutées dans des conditions réelles. La prédiction prend en compte l’optimisation du compilateur. Les résultats sont extrapolables et ils sont obtenus pour un ralentissement réduit. Ce travail de recherche est implémenté dans un logiciel nouveau nommé dPerf. dPerf est capable de prédire les performances des applications C, C++ ou Fortran qui communiquent en utilisant les normes MPI ou P2P-SAP et qui s’exécutent sur une architecture cible pair à pair, hétérogène et décentralisée. La précision de cette contribution a été étudiée sur (i) la transformée Laplace, pour l’aspect séquentiel, (ii) le benchmark IS de NAS, pour l’aspect MPI, (iii) et le code de l’obstacle pour l’aspect calcul P2P décentralisé et l’extrapolation du nombre de nœuds. / In the field of high performance computing, the architectures evolve continuously. In order to increase the number of computing nodes or the network speed, an important investment must be considered, from both temporal and financial point of view. Performance prediction methods aim at assisting in finding the best trade-off for such an investment. At the same time, P2P HPC systems have known an increase in development. These heterogeneous architectures would allow solving scientific problems at a low cost, with respect to dedicated systems.The manuscript presents a new method for performance prediction. This method applies to real applications for distributed computing, considered in a real execution environment. This method uses information about the different compiler optimization levels. The prediction results are obtained with reduced slowdown and are scalable. This thesis took shape in the development of the dPerf tool. dPerf predicts the performances of C, C++, and Fortran application, which use MPI or P2P-SAP to communicate. The applications modeled by dPerf are meant for execution on P2P heterogeneous architectures, with a decentralized communication topology. The accuracy of dPerf has been studied on three applications: (i) the Laplace transform, for sequential codes, (ii) the NAS Integer Sort benchmark for distributed MPI programs, (iii) and the obstacle problem, for the decentralized P2P computing and the scaling of the number of computing nodes.

Nous analysons dans cette thèse différents aspects associés à la modélisation des écoulements à surface libre en eaux peu profondes (Shallow Water). Nous étudions tout d’abord le système d’équations de Saint-Venant à deux dimensions et leur résolution par la méthode numérique des volumes finis, en portant une attention particulière sur les aspects hyperboliques et conservatifs. Ces schémas permettent de traiter les équilibres stationnaires, les interfaces sec/mouillé et aussi de modéliser des écoulements subcritique, transcritique et supercritique. Nous présentons ensuite la théorie de la méthode d’assimilation variationnelle de données adaptée à ce type d’écoulement. Son application au travers des études de sensibilité est longuement discutée dans le cadre de l'hydraulique à surface libre. Après cette partie à caractère théorique, la partie tests commence par une qualification de l’ensemble des méthodes numériques qui sont implémentées dans le code DassFlow, développé à l’Université de Toulouse, principalement à l’IMT mais aussi à l’IMFT. Ce code résout les équations Shallow Water par une méthode de volumes finis et est validé par comparaison avec les solutions analytiques pour des cas tests classiques. Ces mêmes résultats sont comparés avec un autre code d’hydraulique à surface libre aux éléments finis en deux dimensions, Telemac 2D. Une particularité notable du code DassFlow est de permettre l’assimilation variationnelle de données grâce au code adjoint permettant le calcul du gradient de la fonction coût. Ce code adjoint a été obtenu en utilisant l'outil de différentiation automatique Tapenade (Inria). Nous testons ensuite sur un cas réel, hydrauliquement complexe, différentes qualités de Modèles Numériques de Terrain (MNT) et de bathymétrie du lit d’une rivière. Ces informations proviennent soit d’une base de données classique type IGN, soit d’informations LIDAR à très haute résolution. La comparaison des influences respectives de la bathymétrie, du maillage et du type de code utilisé, sur la dynamique d’inondation est menée très finement. Enfin nous réalisons des études cartographiques de sensibilité aux paramètres du modèle sur DassFlow. Ces cartes montrent l’influence respective des différents paramètres ou de la localisation des points de mesure virtuels. Cette localisation optimale de ces points est nécessaire pour une future assimilation de données efficiente. / We analyze in this thesis various aspects associated with the modeling of free surface flows in shallow water approximation. We first study the system of Saint-Venant equations in two dimensions and its resolution with the numerical finite volumes method, focusing in particular on aspects hyperbolic and conservative. These schemes can process stationary equilibria, wetdry interfaces and model subcritical, transcritical and supercritical flows. After, we present the variational data assimilation method theory fitted to this kind of flow. Its application through sensitivity studies is fully discussed in the context of free surface water. After this theoretical part, we test the qualification of numerical methods implemented in the code Dassflow, developed at the University of Toulouse, mainly at l'IMT, but also at IMFT. This code solves the Shallow Water equations by finite volume method and is validated by comparison with analytical solutions for standard test cases. These results are compared with another hydraulic free surface flow code using finite elements in two dimensions: Telemac2D. A significant feature of the Dassflow code is to allow variational data assimilation using the adjoint method for calculating the cost function gradient. The adjoint code was obtained using the automatic differentiation tool Tapenade (INRIA). Then, the test is carried on a real hydraulically complex case using different qualities of Digital Elevation Models (DEM) and bathymetry of the river bed. This information are provided by either a conventional database types IGN or a very high resolution LIDAR information. The comparison of the respective influences of bathymetry, mesh size, kind of code used on the dynamics of flooding is very finely explored. Finally we perform sensitivity mapping studies on parameters of the Dassflow model. These maps show the respective influence of different parameters and of the location of virtual measurement points. This optimal location of these points is necessary for an efficient data assimilation in the future.

This dissertation is a contribution to the development of a unified model of continuum mechanics, describing both fluids and elastic solids as a general continua, with a simple material parameter choice being the distinction between inviscid or viscous fluid, or elastic solids or visco-elasto-plastic media. Additional physical effects such as surface tension, rate-dependent material failure and fatigue can be, and have been, included in the same formalism. The model extends a hyperelastic formulation of solid mechanics in Eulerian coordinates to fluid flows by means of stiff algebraic relaxation source terms. The governing equations are then solved by means of high order ADER Discontinuous Galerkin and Finite Volume schemes on fixed Cartesian meshes and on moving unstructured polygonal meshes with adaptive connectivity, the latter constructed and moved by means of a in- house Fortran library for the generation of high quality Delaunay and Voronoi meshes. Further, the thesis introduces a new family of exponential-type and semi- analytical time-integration methods for the stiff source terms governing friction and pressure relaxation in Baer-Nunziato compressible multiphase flows, as well as for relaxation in the unified model of continuum mechanics, associated with viscosity and plasticity, and heat conduction effects. Theoretical consideration about the model are also given, from the solution of weak hyperbolicity issues affecting some special cases of the governing equations, to the computation of accurate eigenvalue estimates, to the discussion of the geometrical structure of the equations and involution constraints of curl type, then enforced both via a GLM curl cleaning method, and by means of special involution-preserving discrete differential operators, implemented in a semi-implicit framework. Concerning applications to real-world problems, this thesis includes simulation ranging from low-Mach viscous two-phase flow, to shockwaves in compressible viscous flow on unstructured moving grids, to diffuse interface crack formation in solids.