Adaptive multipreconditioned FETI: Scalability results and robustness assessment

Bovet, Christophe; Parret-Fréaud, Augustin; Spillane, Nicole; Gosselet, Pierre

doi:10.1016/j.compstruc.2017.07.010

Cited by 24 publications

(54 citation statements)

References 30 publications

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“…where the right-hand side is the high-fidelity quadrature formula used for numerical evaluation. In (8), the stress tensor σ ( (û µ ), y µ ) for the considered reduced solutionû µ at variability µ and internal variables y µ is seen as a function of space, and E denotes the set of elements of the mesh, n e denotes the number of integration points for the element e, ω k and x k are the integration weights and points of the considered element. The ECM consists in replacing this high-fidelity quadrature (8) by an approximation adapted to the snapshots {u µi } 1≤i≤Nc and the reduced order basis {ψ i } 1≤i≤n , and involving a small number of integration points:…”

Section: Reduced Order Modelingmentioning

confidence: 99%

An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

Casenave

Akkari

2019

MCA

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The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes the classical unenriched proper orthogonal decomposition method fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the error indicator becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.Computing lifetime predictions for high-pressure turbine blades is a challenging task: meshes involve large numbers of degrees of freedom to account for local structures such as the internal cooling channels, the behavior laws are strongly nonlinear with many internal variables, and a large number of cycles has to be computed. Besides, the temperature loading is poorly known in the outlet section of the combustion chamber. Our team has proposed in [12] a nonintrusive reduced order model (ROM) strategy in parallel computation with distributed memory to mitigate the runtime issues: a domain decomposition method is used to compute the first cycle, and the reduced order model is used to speed up the computation of the following cycles, which can be considered as a reduced order model-based temporal extrapolation. As pointed out in [12], errors are accumulated during this temporal extrapolation. Moreover, quantifying the uncertainty on the lifetime with respect to some statistical description of the temperature loading using an already constructed reduced order model would introduce additional errors. In this context, error indicator-based enrichment of reduced order models is the topic of the present work.Error estimation for reduced model predictions is a topic that receives interest in the scientific literature. The reduced basis method [32,28] for parametrized problems is a reduced order modeling method that intrinsically relies on efficient a posteriori error bounds of the error between the reduced prediction and the reference high-fidelity (HF) solution. This method consists in a greedy enrichment of a current reduced order basis by the high-fidelity solution at the parametric...

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Section: Reduced Order Modelingmentioning

confidence: 99%

An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

Casenave

Akkari

2019

MCA

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“…They also offer a framework where efficient iterative solvers can be implemented. In particular recent progress made it possible to design solvers with controlled convergence rate for linear symmetric positive definite systems for many DDM: see for instance [1] for overlapping methods, [2] for FETI and BDD methods, [3,4,5] for FETI-DP and BDDC; also multipreconditioning proved to be an efficient alternative [6] with possible application in more general contexts [7]. This paper focuses on problems involving frictionous contact between parts in small strain.…”

Section: Introductionmentioning

confidence: 99%

A parallel non-invasive mixed domain decomposition - Implementation and applications to mechanical assemblies

Oumaziz

Gosselet

Boucard

et al. 2019

Finite Elements in Analysis and Design

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“…In recent years, different approaches for the construction of adaptive coarse spaces for domain decomposition methods have been studied extensively; see, e.g., [6,7,61,76,23,24,65,66,13,62,87,78,80,81,82,11,79,28,47,49,50,69,27,39,40,89,25,31,1,4,67,9,90,68,38,14,8,44,59,10].…”

Section: Introductionmentioning

confidence: 99%

“…However, parallel implementations of such adaptive coarse spaces [35,87,78,34,36,89,29,8,59] are not simple and are therefore still less common; see also the parallel implementation of the closely related ACMS special finite element method in [30]. Our work is mainly focussed on adaptive FETI-DP methods.…”

Section: Introductionmentioning

confidence: 99%

Parallel adaptive FETI‐DP using lightweight asynchronous dynamic load balancing

Klawonn

Kühn

Rheinbach

2019

Numerical Meth Engineering

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A parallel FETI-DP domain decomposition method using an adaptive coarse space is presented. The implementation builds on a recently introduced adaptive FETI-DP approach for elliptic problems in three dimensions and uses small, local eigenvalue problems for faces and, additionally, for a small number of edges. The condition number of the preconditioned operator then satisfies a bound which is independent of coefficient heterogeneities in the problem. The computational cost of the local eigenvalue problems is not negligible, and also a significant load imbalance can be introduced. As a remedy, certain eigenvalue problems are discarded by a theory-guided heuristic strategy, based on the diagonal entries of the stiffness matrices. Additionally, a lightweight pairwise dynamic load balancing strategy is implemented for the eigenvalue problems. The load balancing is supervised by an orchestrating rank using asynchronous point-to-point communication. The resulting method shows good weak and strong scalability up to thousands of cores while fast convergence is obtained even for heterogeneous problems.

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Adaptive multipreconditioned FETI: Scalability results and robustness assessment

Cited by 24 publications

References 30 publications

An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

An Error Indicator-Based Adaptive Reduced Order Model for Nonlinear Structural Mechanics—Application to High-Pressure Turbine Blades

A parallel non-invasive mixed domain decomposition - Implementation and applications to mechanical assemblies

Parallel adaptive FETI‐DP using lightweight asynchronous dynamic load balancing

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