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Fast estimation of discretization error for FE problems solved by domain decomposition
Authors:A Parret-Fréaud  C Rey  P Gosselet  F Feyel
Affiliation:1. LMT-Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud, 61 av. du président, Wilson, 94235 Cachan cedex, France;2. ONERA, DMSM/CEMN, 29 avenue de la division Leclerc, BP 72, F92322 Chatillon cedex, France;1. School of Mechanics, Civil Engineering, and Architecture, Northwestern Polytechnical University, Xi''an 710129, China;2. Department of Engineering Mechanics, School of Science, Xi''an University of Technology, Xi''an 710048, China;1. Faculty of Physics, University of Seville, Avda. Reina Mercedes s/n, 41012 Seville, Spain;2. LUNAM Université, Université du Maine, CNRS UMR 6613, LAUM, Avenue Olivier Messiaen, 72805 Le Mans Cedex 9, France;1. University of California, Department of Civil and Environmental Engineering, Berkeley, CA 94720, United States;2. University of California, Computer Science Division, Berkeley, CA 94720, United States;1. Argonne National Laboratory, USA;2. Ecole Normale Superieure de Lyon & INRIA, France;3. Jaypee Institute of Information Technology, India;4. University of Tennessee Knoxville, USA;1. Université de Lorraine, Institut Jean Lamour, UMR CNRS 7198, BP 70239, F-54506 Vandoeuvre-lès-Nancy, France;2. Armenian State Pedagogical University, Yerevan, Tigran Mets Ave., 17, Armenia;3. Institute for Physical Researches, National Academy of Sciences of Armenia, Ashtarak-2, Armenia;4. Université de Lorraine, LMOPS, EA 4423, F-57070 Metz, France;5. CentraleSupelec, LMOPS, F-57070 Metz, France
Abstract: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.
Keywords:
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