Publication de 6 numéros par an
ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352
Indexed in
A Nonlinear Dual-Domain Decomposition Method: Application to Structural Problems with Damage
RÉSUMÉ
A dual-domain decomposition method dedicated to nonlinear problems is presented. The decomposition is introduced in the nonlinear formulation, and the nonlinear problem is first condensed on the interface then solved by a Newton-type method. Considering the specificities of the introduced operators, the algorithm can be interpreted as a local/global strategy with global Newton-type iterations and nonlinear relocalizations per subdomain. Such a strategy is particularly interesting in cases where the nonlinearity is localized. First results are presented on structural problems with damage.
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Kerfriden Pierre, Allix O., Gosselet P., A three-scale domain decomposition method for the 3D analysis of debonding in laminates, Computational Mechanics, 44, 3, 2009. Crossref
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Allix O., Kerfriden P., Gosselet P., On the control of the load increments for a proper description of multiple delamination in a domain decomposition framework, International Journal for Numerical Methods in Engineering, 83, 11, 2010. Crossref
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Passieux J.-C., Ladevèze P., Néron D., A scalable time–space multiscale domain decomposition method: adaptive time scale separation, Computational Mechanics, 46, 4, 2010. Crossref
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Gendre L., Allix O., Gosselet P., A two-scale approximation of the Schur complement and its use for non-intrusive coupling, International Journal for Numerical Methods in Engineering, 87, 9, 2011. Crossref
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Lloberas-Valls O., Rixen D.J., Simone A., Sluys L.J., Multiscale domain decomposition analysis of quasi-brittle heterogeneous materials, International Journal for Numerical Methods in Engineering, 89, 11, 2012. Crossref
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Confalonieri Federica, Ghisi Aldo, Cocchetti Giuseppe, Corigliano Alberto, A domain decomposition approach for the simulation of fracture phenomena in polycrystalline microsystems, Computer Methods in Applied Mechanics and Engineering, 277, 2014. Crossref
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Kerfriden P, Gosselet P, Adhikari S, Bordas S, Passieux J-C, POD-based model order reduction for the simulation of strong nonlinear evolutions in structures: Application to damage propagation, IOP Conference Series: Materials Science and Engineering, 10, 2010. Crossref
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Hinojosa J., Allix O., Guidault P.-A., Cresta Ph., Domain decomposition methods with nonlinear localization for the buckling and post-buckling analyses of large structures, Advances in Engineering Software, 70, 2014. Crossref
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Duval Mickaël, Passieux Jean-Charles, Salaün Michel, Guinard Stéphane, Non-intrusive Coupling: Recent Advances and Scalable Nonlinear Domain Decomposition, Archives of Computational Methods in Engineering, 23, 1, 2016. Crossref
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Klawonn Axel, Lanser Martin, Rheinbach Oliver, Nonlinear FETI-DP and BDDC Methods, SIAM Journal on Scientific Computing, 36, 2, 2014. Crossref
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Kawabata Celia Leiko Ogawa, Neto Masaki Kawabata, Coda Humberto Breves, Venturini Wilson Sergio, Finite Element Nodal Approach for Parallel Processing of Non Linear Shell Analysis, 2009 21st International Symposium on Computer Architecture and High Performance Computing, 2009. Crossref
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Kerfriden P., Gosselet P., Adhikari S., Bordas S.P.A., Bridging proper orthogonal decomposition methods and augmented Newton–Krylov algorithms: An adaptive model order reduction for highly nonlinear mechanical problems, Computer Methods in Applied Mechanics and Engineering, 200, 5-8, 2011. Crossref
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Klawonn Axel, Lanser Martin, Rheinbach Oliver, Toward Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations, SIAM Journal on Scientific Computing, 37, 6, 2015. Crossref
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Kim J., Duarte C. A., A new generalized finite element method for two-scale simulations of propagating cohesive fractures in 3-D, International Journal for Numerical Methods in Engineering, 104, 13, 2015. Crossref
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Plews J. A., Duarte C. A., A two-scale generalized finite element approach for modeling localized thermoplasticity, International Journal for Numerical Methods in Engineering, 108, 10, 2016. Crossref
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Yang Haijian, Yang Chao, Sun Shuyu, Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media, SIAM Journal on Scientific Computing, 38, 4, 2016. Crossref
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Negrello Camille, Gosselet Pierre, Rey Christian, Pebrel Julien, Substructured formulations of nonlinear structure problems - influence of the interface condition, International Journal for Numerical Methods in Engineering, 107, 13, 2016. Crossref
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Hinojosa J., Allix O., Guidault P. A., Cresta Ph., Saavedra K., Mixed nonlinear localization strategy for the buckling and post-buckling analyses of structures: parameter optimization and path following implementation, Engineering Optimization, 49, 2, 2017. Crossref
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Klawonn Axel, Lanser Martin, Rheinbach Oliver, A Highly Scalable Implementation of Inexact Nonlinear FETI-DP Without Sparse Direct Solvers, in Numerical Mathematics and Advanced Applications ENUMATH 2015, 112, 2016. Crossref
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Klawonn Axel, Lanser Martin, Rheinbach Oliver, Uran Matthias, Nonlinear FETI-DP and BDDC Methods: A Unified Framework and Parallel Results, SIAM Journal on Scientific Computing, 39, 6, 2017. Crossref
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Saavedra K., Allix O., Gosselet P., Hinojosa J., Viard A., An enhanced nonlinear multi-scale strategy for the simulation of buckling and delamination on 3D composite plates, Computer Methods in Applied Mechanics and Engineering, 317, 2017. Crossref
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Yusa Yasunori, Okada Hiroshi, Yamada Tomonori, Yoshimura Shinobu, Scalable parallel elastic–plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner, Computational Mechanics, 62, 6, 2018. Crossref
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Negrello Camille, Gosselet Pierre, Rey Christian, A new impedance accounting for short- and long-range effects in mixed substructured formulations of nonlinear problems, International Journal for Numerical Methods in Engineering, 114, 7, 2018. Crossref
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Liu Yanjie, Sun Qin, Kontis K., Pantelakis S., A Two-Level Non-Intrusive Coupling Method for Fatigue Analysis, MATEC Web of Conferences, 233, 2018. Crossref
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Allix Olivier, Gendre Lionel, Gosselet Pierre, Guguin Guillaume, Non-intrusive Coupling: An Attempt to Merge Industrial and Research Software Capabilities, in Recent Developments and Innovative Applications in Computational Mechanics, 2011. Crossref
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Klawonn Axel, Köhler Stephan, Lanser Martin, Rheinbach Oliver, Computational homogenization with million-way parallelism using domain decomposition methods, Computational Mechanics, 65, 1, 2020. Crossref
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Klawonn Axel, Lanser Martin, Rheinbach Oliver, A Nonlinear FETI-DP Method with an Inexact Coarse Problem, in Domain Decomposition Methods in Science and Engineering XXII, 104, 2016. Crossref
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van der Valk Paul L. C., Rixen Daniel J., Towards a Parallel Time Integration Method for Nonlinear Systems, in Dynamics of Coupled Structures, Volume 1, 2014. Crossref
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Gendre Lionel, Allix Olivier, Gosselet Pierre, Comte François, Non-intrusive and exact global/local techniques for structural problems with local plasticity, Computational Mechanics, 44, 2, 2009. Crossref
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Haeberlein Florian, Halpern Laurence, Michel Anthony, Newton-Schwarz Optimised Waveform Relaxation Krylov Accelerators for Nonlinear Reactive Transport, in Domain Decomposition Methods in Science and Engineering XX, 91, 2013. Crossref
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Klawonn Axel, Lanser Martin, Uran Matthias, Rheinbach Oliver, Köhler Stephan, Schröder Jörg, Scheunemann Lisa, Brands Dominik, Balzani Daniel, Gandhi Ashutosh, Wellein Gerhard, Wittmann Markus, Schenk Olaf, Janalík Radim, EXASTEEL: Towards a Virtual Laboratory for the Multiscale Simulation of Dual-Phase Steel Using High-Performance Computing, in Software for Exascale Computing - SPPEXA 2016-2019, 136, 2020. Crossref
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Heinlein Alexander, Lanser Martin, Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids, SIAM Journal on Scientific Computing, 42, 4, 2020. Crossref
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Peña Larry, Hinojosa Jorge, Implementation of a new expression for the search direction in simulations of structures with buckling and post-buckling: ”Two-Scale Impedance”, Journal of Computational and Applied Mathematics, 403, 2022. Crossref
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Ajith Gopika, Ghosh Debraj, A novel method for solving nonlinear stochastic mechanics problems using FETI‐DP, International Journal for Numerical Methods in Engineering, 123, 10, 2022. Crossref
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Liu Lulu, Hwang Feng-Nan, Luo Li, Cai Xiao-Chuan, Keyes David E., A Nonlinear Elimination Preconditioned Inexact Newton Algorithm, SIAM Journal on Scientific Computing, 44, 3, 2022. Crossref
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Köhler Stephan, Rheinbach Oliver, Globalization of Nonlinear FETI-DP Domain Decomposition Methods Using an SQP Approach, Vietnam Journal of Mathematics, 2022. Crossref
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Fuenzalida-Henriquez Ignacio, Hinojosa Jorge, Peña Larry, Astudillo Cesar, Optimizing the search directions of a mixed DDM applied on cracks, Optimization and Engineering, 23, 3, 2022. Crossref
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Heinlein Alexander, Klawonn Axel, Lanser Martin, Adaptive Nonlinear Domain Decomposition Methods with an Application to the $p$-Laplacian, SIAM Journal on Scientific Computing, 2022. Crossref