New implementations for the Simultaneous‐FETI method

International audienceIn this work, we present alternative implementations for the Simultaneous‐FETI (S‐FETI) method. Developed in recent years, this method has shown to be very robust for highly heterogeneous problems. However, the memory cost in S‐FETI is greatly increased and can be a limitation to its use. Our main objective is to reduce this memory usage without losing significant time performance. The algorithm is based on the exploitation of the sparsity patterns found on the block of search directions, allowing to store less vectors per iteration in comparison to a full storage scheme. In addition, different variations for the S‐FETI method are also proposed, including a new treatment for the possible dependencies between directions and the use of the Lumped preconditioner. Several tests are performed in order to establish the impact of the modifications presented in this work compared to the original S‐FETI algorithm.Cet article présente une nouvelle mise en œuvre de la méthode S-FETI qui permet de l'appliquer à des problèmes industriels de plus grande taille. La méthode S-FETI permet de traiter de manière robuste des problèmes fortement hétérogènes. Cependant elle présente un coût de stockage élevé susceptible de limiter son application.La nouvelle méthode utilise le caractère creux des blocs de directions de descente construits à chaque itération pour limiter le stockage. De plus une nouvelle façon de traiter les dépendances entre directions de descente ou d'utiliser le préconditionneur "lumped" pour S-FETI est présentée.Des tests numériques comparent les nouvelles méthodes développées dans cet article avec la méthode S-FETI initiale

Mise en œuvre d'un solveur direct parallèle pour l'inversion des problèmes locaux au sein d'une méthode de décomposition de domaine

National audienceLe but de ce papier est de mettre au point un algorithme parallèle pour la résolution directe de grands systèmes linéaires creux et l’intégrer dans les méthodes de décomposition de domaine. Ces systèmes linéaires, souvent rencontrés lor de la simulation numérique de problèmes de mécanique des structures par des codes de calcul par éléments finis, sont résolus avec des coûts très importants en temps ce calcul et en espace mémoire. Dans ce papier, un parallélisme à deux niveaux a été exploité. L’exploitation du niveau inférieur de parallélisme a d’abord consisté à réaliser un solveur direct parallèle basé sur une technique de dissection emboitée et l’intégrer ensuite dans les méthodes FETI. Ce solveur direct a l’avantage de traiter automatiquement et proprement les modes à énergie nulle dans des structures flottantes. L’exploitation du niveau supérieur a consisté à améliorer la phase itérative de la méthode FETI classique. Des tests ont été effectués pour évaluer les performances du solveur mis en place

L’adaptation des juridictions

Le droit animalier fait l’objet d’un intéressement de plus en plus important de la part des citoyens. En France, les élections sont un révélateur de cet intérêt grandissant. Devenant une préoccupation pour beaucoup d’électeurs français, la cause animale entre alors dans le débat électoral. Avec toutes les réserves à apporter aux sondages, les résultats d’une enquête IFOP parus en mars 2022 révèlent que 81 % des Français sont sensibles au bien-être animal. En conséquence, il n’est pas surprena..

Simultaneous-FETI and Block-FETI: robust domain decomposition with multiple search directions.

International audienceDomain Decomposition methods often exhibit very poor performance when applied to engineering problems with large heterogeneities. In particular for heterogeneities along domain interfaces the iterative techniques to solve the interface problem are lacking an efficient preconditioner. Recently a robust approach, named FETI-Geneo, was proposed where troublesome modes are precomputed and deflated from the interface problem. The cost of the FETI-Geneo is however high. We propose in this paper techniques that share similar ideas with FETI-Geneo but where no pre-processing is needed and that can be easily and efficiently implemented as an alternative to standard Domain Decomposition methods. In the block iterative approaches presented in this paper, the search space at every iteration on the interface problem contains as many directions as there are domains in the decomposition. Those search directions originate either from the domain-wise preconditioner (in the Simultaneous FETI method) or from the block structure of the right-hand side of the interface problem (Block FETI). We show on 2D structural examples that both methods are robust and provide good convergence in the presence of high heterogeneities, even when the interface is jagged or when the domains have a bad aspect ratio. The Simultaneous FETI was also efficiently implemented in an optimized parallel code and exhibited excellent performance compared to the regular FETI method

Parallel Computational Acoustics Library - Mesh Generation Reference Manual

Rapport interne.Mesh Generation Reference Manua

Parallel Computational Acoustics Library - Reference Manual

Rapport interne.Reference Manua

Parallel Computational Acoustics Library - User's Guide

Rapport interne.Parallel Computational Acoustics Library - User's Guid

Unsatisfactory outcomes in myasthenia gravis: influence by care providers

Myasthenia gravis (MG) can be difficult to treat despite an available therapeutic armamentarium. Our aim was to analyze the factors leading to unsatisfactory outcome (UO). To this end we used the Myasthenia Gravis Foundation of America classification system. Forty one patients with autoimmune MG were followed prospectively from January 2003 to December 2007. Outcomes were assessed throughout follow-up and at a final visit. ‘Unchanged', ‘worse', ‘exacerbation' and ‘died of MG' post-intervention status were considered UOs. During follow-up, UO rates reached 54% and were related to undertreatment (41%), poor treatment compliance (23%), infections (23%), and adverse drug effects (13%). The UO rate at final study assessment was 20%. UO during follow-up was significantly (P=0.004) predictive of UOs at final assessment. When care was provided by neuromuscular (NM) specialists, patients had significantly better follow-up scores (P=0.01). At final assessment UO rates were 7% and significantly better in patients treated by NM specialists, compared to other physicians where UO rates reached 27%. UO was a frequent finding occurring in more than half our patients during follow-up. Nearly two-thirds of the UOs could have been prevented by appropriate therapeutic adjustments and improved compliance. The differential UO rates at follow-up, their dependency on the degree to which the management was specialized and their correlation with final outcomes suggest that specialized MG care improves outcome

A non Overlapping Domain Decomposition Method for the Exterior Helmholtz Problem

In this paper, we first show that the domain decomposition methods that are usually efficient for solving elliptic problems typically fail when applied to acoustics problems.Next, we present an alternative domain decomposition algorithm that is better suited for the exterior Helmholtz problem. We describe it in a formalism that can use either one or two Lagrange multiplier fields for solving the corresponding interface problem by a Krylov method. In order to improve convergence and ensure scalability with respect the number of subdomains, we propose two complementary preconditioning techniques. The first preconditioner is based on a spectral analysis of the resulting interface operator and targets the high frequency components of the error. The second preconditioner is based on a coarsening technique, employs plane waves, and addresses the low frequency components of the error. Finally, we show numerically that, using both preconditioners, the convergence rate of the proposed domain decomposition method is quasi independent of the number of elements in the mesh, the number of subdomains, and depends only weakly on the wavenumber, which makes this method uniquely suitable for solving large-scale high frequency exterior acoustics problems