, Pour mesurer cette dernière, les déplacements et la pression après convergence sont comparés aux valeurs calculées par la résolution monolithique. Enfin, on mesure le nombre moyen d'itérations des sous-solveurs pour une itération externe. Les résultats sont rassemblés dans le tableau 6.6. Si la tolérance interne est trop permissive par rapport à la tolérance externe, alors la méthode fixed-stress converge très rapidement vers une mauvaise solution. Lorsque la tolérance interne diminue, la convergence de la méthode fixed-stress nécessite plus d'itérations mais la précision des solutions s'améliore. En toute logique, ces deux quantités tendent vers un palier correspondant aux résultats obtenus avec un sous-solveur direct pour les sous-problèmes. Diminuer la tolérance interne améliore la solution, mais augmente le coût global de la résolution : non seulement le nombre d'itérations externes est plus élevé, mais le nombre d'itérations internes augmente également. Au vu de ces résultats, la tolérance interne doit être au moins de deux ordres de grandeur inférieure à la tolérance externe. En revanche, à partir de 4 ordres de grandeurs d'écart, l'amélioration de la solution semble insuffisante vis-à-vis de l'augmentation du nombre d'itérations des sous-solveurs, Les sous-solveurs qualifiés pour la résolution des sous-problèmes étant maintenant utilisables, il reste à régler leurs paramètres, typiquement leur tolérance int , et à vérifier leur comportement dans le cadre de la stratégie séquentielle fixed-stress

. Enfin, deux actions sont envisageables. La première consisterait à réduire à nouveau le coût de la stratégie fixed-stress : par exemple en utilisant un pas de temps différent pour chaque sous-problème (la partie mécanique, plus coûteuse à résoudre, évoluant moins rapidement que la partie écoulement), en suivant la méthodologie développée dans, Alm+16

, ou bien en travaillant sur une version parallèle en temps de la méthode, en se basant sur les travaux récents, vol.19

, La seconde serait de rester sur une résolution monolithique du système, en tentant d'y appliquer une méthode de décomposition de domaine à deux niveaux

, Réalisations et publications

, en utilisant la méthode des éléments virtuels pour l'équation d'élasticité et une méthode de volumes finis à deux points ou multipoints pour l'(éventuelle) équation d'écoulement. Pour le problème de poroélasticité, le choix d'une résolution monolithique ou séquentielle par la méthode fixed-stress split est laissé à l'utilisateur, qui peut dans le second cas choisir entre une méthode de type point fixe, l'algorithme BiCGStab ou l'algorithme Gmres pour les itérations de couplage. La résolution peut être effectuée par l'un des solveurs de PETSc interfacé avec la plateforme ou, pour le (sous-)problème d'élasticité, en laissant le module générer les objets nécessaires à la décomposition de domaine. De plus, le module tire parti de plusieurs briques de base de la plateforme pour proposer des fonctionnalités avancées, parmi lesquelles : gestion (partielle) de maillages évolutifs variant au cours du temps, coefficients physiques hétérogènes, prise en compte de plusieurs types de conditions aux limites possiblement différentes dans chaque direction (pour la mécanique) et sur chaque groupe de faces de bord, analyse syntaxique de fonctions analytiques pour les données d'entrée du problème, parallélisation Mpi, Concrètement, la valorisation de ces travaux de thèse se retrouve sous deux formes : la mise à la disposition des équipes de recherche d'ifpen d'un module de calcul dans la plateforme de simulation Arcane, et plusieurs communications scientifiques. Le module de calcul développé permet la résolution du problème élastique ou poroélastique sur des maillages polyédriques bidimensionnels ou tridimensionnels

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, ? Coupling Virtual Element Methods and Finite Volume Schemes for, Computational Geomechanics on General Meshes

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, ? Fully Coupled Schemes Using Virtual Element And Finite Volume Discretisations For Biot Equations Modelling

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