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 strategy for a posteriori error estimation for substructured problems solved by non-overlapping domain decomposition methods. We focus on global estimates of the discretization error obtained through the error in constitutive relation for linear mechanical problems. Our method allows to compute error estimate in a fully parallel way for both primal (BDD) and dual (FETI) approaches of non-overlapping domain decomposition whatever the state (converged or not) of the associated iterative solver. Results obtained on an academic problem show that the strategy we propose is efficient in the sense that correct estimation is obtained with fully parallel computations; they also indicate that the estimation of the discretization error reaches sufficient precision in very few iterations of the domain decomposition solver, which enables to consider highly effective adaptive computational strategies.

This paper investigates the question of the building of admissible stress field in a substructured context. More precisely we analyze the special role played by multiple points. This study leads to (1) an improved recovery of the stress field, (2) an opportunity to minimize the estimator in the case of heterogeneous structures (in the parallel and sequential case), (3) a procedure to build admissible fields for FETI-DP and BDDC methods leading to an error bound which separates the contributions of the solver and of the discretization.

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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.

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.

This paper describes a new approach in order to formulate well-posed timedomain damping models able to represent various frequency domain profiles of damping properties. The novelty of this approach is to represent the behavior law of a given material directly in a discrete-time framework as a digital filter, which is synthesized for each material from a discrete set of frequency-domain data such as complex modulus through an optimization process. A key point is the addition of specific constraints to this process in order to guarantee stability, causality and verification of thermodynamics second law when transposing the resulting discrete-time behavior law into the time domain. Thus, this method offers a framework which is particularly suitable for time-domain simulations in structural dynamics and acoustics for a wide range of materials (polymers, wood, foam...), allowing to control and even reduce the distortion effects induced by time-discretization schemes on the frequency response of continuous-time behavior laws.

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