The purpose of this article is to assess the adaptive multipreconditioned FETI solvers (AMPFETI) on realistic industrial problems and hardware. The multipreconditioned FETI algorithm (first introduced as Simultaneous FETI [1]) is a non-overlapping domain decomposition method which exhibits good robustness properties without requiring the explicit knowledge of the original partial differential equation, or any a priori analysis of the algebraic system through eigenvalues problems. Multipreconditioned FETI solves critical problems in significantly fewer iterations than classical FETI but each iteration involves a larger computational effort. An adaptive strategy (known as the adaptive multipreconditioned conjugate gradient algorithm [2]) has been proposed to achieve balance between robustness and efficiency and we will observe that it provides an efficient solver for the problems considered here.

This paper presents a modelling approach for predicting the internal dynamic behaviour of ball bearings under high moment loads. This type of loading is a specific feature of helicopter main gear boxes because of special design rules and the high structural flexibility of such systems. The ball bearing model proposed here is not limited to planar systems and incorporates several different phenomena such as contact deformation, elastohydrodynamic contact, internal clearance and cage run-out. The cage-race interaction is treated as a hybrid short journal model, which ensures continuity of the contact force at the transition from the hydrodynamic to metal-to-metal regime. In the dynamic analysis of such a severely loaded bearing, the dependence of the shaft-to-inner-ring force on inner race position cannot be neglected. An equivalent viscoelastic hinge joint has been developed, it produces an additional force that represents the overall rigidity of the system. The stiffness parameters of the joint are identified using global finite element simulations. A ball bearing loaded with two different moments is chosen as an example. Relevant results concerning the internal dynamic behaviour are given. The predicted cage trajectory has been compared to experimental observations, and good agreement has been found.

This article introduces two strategies to reduce the memory cost of the Adaptive Multipreconditioned FETI method (AMPFETI) while preserving its capability to solve ill conditioned systems efficiently. Their common principle is to gather search directions into aggregates which are frequently adapted in order to achieve the best compromise between the decrease of the solver error and the computational resources employed. The methods are assessed on two weak scalability studies on highly heterogeneous problems up to 10368 cores and half a billion of unknowns, and on two illconditioned industrial applications, related to the numerical homogenization of solid propellant and to the simulation of a multiperforated aircraft combustion chamber.

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-This work presents the dynamic modeling of ball bearing which uses multibody dynamic formalism. Such formalism allows immediate integration of the model in dynamic simulations of helicopter main gear boxes. Ball bearing is considered non-lubricated in order to predict its behavior in case of lubrication system failure. Rolling contacts are treated with the method proposed by Kalker. This approach is based on polynomial approximation of relative displacement on the contact ellipse. For low computational cost and without any spatial discretization, it gives a good estimation of tangential traction and creep. Also, a regularization of the Kalker linear creep theory is proposed. It is used here to facilitate the global convergence of the Newton iterative process. It is well suited for multibody dynamic simulations which do not need a very fine treatment of rolling contact. A numerical example of a ball bearing under thrust load is presented. Key words: Multibody dynamic / Ball bearing / Rolling contact / Kalker creep theoryRésumé -Cetteétude présente un modèle dynamique de roulementà billes utilisant le formalisme de la dynamique multicorps. Ce dernier permet l'intégration immédiate du modèle dans les simulations dynamiques de boîtes de transmission de puissance d'hélicoptères. Le roulement est considéré non lubrifié afin de prédire son comportement en cas de défaillance du système de lubrification. Le modèle mis en place pour les contacts roulants pseudo-ponctuels, issu des travaux de J.J. Kalker, se fonde sur une approximation polynomiale du déplacement relatif sur l'ellipse de contact. Ce dernier fournit, pour un temps de calcul réduit et sans discrétisation spatiale, une bonne estimation des efforts et micro-glissements au contact. Aussi, une régularisation de la théorie linéaire de Kalker est proposée. Elle est utilisée pour faciliter la convergence globale de l'algorithme de Newton. Elle estégalement bien adaptée aux simulations dynamiques multicorps qui ne nécessitent pas une modélisation très fine du contact roulant. Un roulementà billes soumisà un effort axial est présenté comme exemple numérique.

This paper presents a new parallel mesh generation method leading to subdomains of shape well-suited to Schur based domain decomposition methods such as the FETI and BDD solvers. Starting from a coarse mesh, subdomains meshes are created in parallel through hierarchical mesh refinement and morphing techniques. The proposed methodology aims at limiting the occurrence of known pathological situations (jagged interfaces, misplaced heterogeneity with respect to the interfaces, . . . ) that penalize the convergence of the solver. Furthermore, it enables to distribute and parallelize the mesh generation step in the early phases of the whole analysis. Besides its good behavior towards convergence, the mesh generation is thus distributed. The method is assessed, on several academical and industrial test cases, for both its parallel efficiency when creating the mesh and its capability to generate decomposition resulting in less FETI iterations.

Solving highly heterogeneous structural mechanic problems with a large number of degrees of freedom (HPC simulations) is a real issue in engineering work, because of the required time and memory. Non overlapping domain decomposition methods such as the Finite Element Tearing and Interconnecting (FETI) or Balanced Domain Decomposition (BDD) methods have been developed in order to allocate the problems on distributed memory clusters with a large number of processors and to make mechanical calculations parallel.Two difficulties are encountered when applying domain decomposition methods. First, the mesh generation is most often a sequential process applied to the full domain. Second, the linear system resulting from the partitioning of the mesh may be poorly conditioned, leading to slow convergence. Recently developed techniques such as adapted coarse spaces (e.g. FETI-GenEO) or multipreconditioning (e.g. AMPFETI) enable to restore good convergence rate, at the cost of extra computations.In this study, we try to mitigate these two difficulties by proposing a new hierarchical substructuring method which aims at making the mesh preprocessing step parallel and at improving the condition number of the linear system to be solved by generating regular interfaces adapted to the heterogeneity.

This article introduces a robust and affordable method to compute nullspace and generalized inverse of finite element operators involved in dual domain decomposition methods. The methodology relies on the operator partial factorization and on the analysis of a well chosen Schur complement. The sparse linear operator is interpreted as a network and graph centrality measures are used to select the condensation variables. Eigen vector, Katz and Page Rank centralities are evaluated. An extension to deal with symmetric indefinite systems arising from mixed finite elements is also presented. The approach is assessed on highly heterogeneous problems and one industrial application is presented: the numerical homogenization of solid propellant.