Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
MTZ-Fachkongress

Antriebe und Energiesysteme von morgen


Austausch von Automobil- und Energiewirtschaft

Am 14./15. Mai geht es in Chemnitz um die Mobilitätswende durch Elektro- und Wasserstofffahrzeuge.
Erweiterte Suche
Anmelden
nach oben
Computational Mechanics
Erschienen in: Computational Mechanics 2/2015

01.02.2015 | Original Paper

A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework

verfasst von: E. Nadal, A. Leygue, F. Chinesta, M. Beringhier, J. J. Ródenas, F. J. Fuenmayor

Erschienen in: Computational Mechanics | Ausgabe 2/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Today industries do not only require fast simulation techniques but also verification techniques for the simulations. The proper generalized decomposition (PGD) has been situated as a suitable tool for fast simulation for many physical phenomena. However, so far, verification tools for the PGD are under development. The PGD approximation error mainly comes from two different sources. The first one is related with the truncation of the PGD approximation and the second one is related with the discretization error of the underlying numerical technique. In this work we propose a fast error indicator technique based on recovery techniques, for the discretization error of the numerical technique used by the PGD technique, for refinement purposes.
Vorheriger Artikel Thanks to our reviewers
Nächster Artikel A rate-dependent stochastic damage–plasticity model for quasi-brittle materials

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Literatur
1.
Ammar A, Mokdad B, Chinesta F, Keunings R (2006) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modeling of complex fluids. J Non-Newton Fluid Mech 139:153–176CrossRefMATH
2.
Ammar A, Mokdad B, Chinesta F, Keunings R (2007) A new family of solvers for some classes of multidimensional partial differential equations encountered in kinetic theory modelling of complex fluids. J Non-Newton Fluid Mech 144:98–121CrossRefMATH
3.
Chinesta F, Ladeveze P, Cueto E (2011) A short review on model order reduction based on proper generalized decomposition. Arch Comput Methods Eng 18:395–404CrossRef
4.
Giner E, Bognet B, Ródenas JJ, Leygue A, Fuenmayor FJ, Chinesta F (2013) The proper generalized decomposition (PGD) as a numerical procedure to solve 3D cracked plates in linear elastic fracture mechanics. Int J Solids Struct 50:1710–1720CrossRef
5.
Chinesta F, Ammar A, Leygue A, Keunings R (2011) An overview of the proper generalized decomposition with applications in computational rheology. J Non-Newton Fluid Mech 166(11):578–592CrossRefMATH
6.
Ammar A, Chinesta F, Diez P, Huerta A (2010) An error estimator for separated representations of highly multidimensional models. Comput Methods Appl Mech Eng 199(25–28):1872–1880CrossRefMathSciNetMATH
7.
Moitinho de Almeida JP (2013) A basis for bounding the errors of proper generalised decomposition solutions in solid mechanics. Int J Numer Methods Eng 94:961–984CrossRefMathSciNet
8.
Ladevèze P, Chamoin L (2011) On the verification of model reduction methods based on the proper generalized decomposition. Comput Methods Appl Mech Eng 200:2032–2047CrossRefMATH
9.
Ladevèze P, Leguillon D (1983) Error estimate procedure in the finite element method and applications. SIAM J Numer Anal 20(3):485–509CrossRefMathSciNetMATH
10.
Babuška I, Rheinboldt WC (1978) A-posteriori error estimates for the finite element method. Int J Numer Methods Eng 12(10):1597–1615CrossRefMATH
11.
Ródenas JJ, Tur M, Fuenmayor FJ, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70(6):705–727CrossRefMATH
12.
Díez P, Parés N, Huerta A (2003) Recovering lower bounds of the error by postprocessing implicit residual a posteriori error estimates. Int J Numer Methods Eng 56(10):1465–1488CrossRefMATH
13.
Bognet B, Bordeu F, Chinesta F, Leygue A, Poitou A (2012) Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity. Comput Methods Appl Mech Eng 201–204:1–12CrossRef
14.
Bognet B, Leygue A, Chinesta F (2014) Separated representations of 3D elastic solutions in shell geometries. Adv Model Simul Eng Sci 1(1):1–4CrossRef
15.
Ghnatios C, Chinesta F, Binetruy C (2013) 3D modeling of squeeze flows occurring in composite laminates. Int J Mater Form 9(1):1–11
16.
Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numer Methods Eng 24(2):337–357CrossRefMathSciNetMATH
17.
Chinesta F, Keunings R, Leygue A (2013) The proper generalized decomposition for advanced numerical simulations: a primer. Springer Publishing Company, New York Incorporated
18.
Donea J, Huerta A (2002) Finite element methods for flow problems. Wiley, New York
19.
Gonzalez D, Cueto E, Chinesta F, Diez P, Huerta A (2013) SUPG-based stabilization of proper generalized decompositions for high-dimensional advection-diffusion equations. Int J Numer Methods Eng 94(13):1216–1232CrossRefMathSciNet
20.
Chinesta F, Ammar A, Cueto E (2010) Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models. Arch Comput Methods Eng 17(4):327–350
21.
Chinesta F, Leygue A, Bordeu F, Aguado JV, Cueto E, Gonzalez D, Alfaro I, Ammar A, Huerta A (2013) PGD-based computational vademecum for efficient design, optimization and control. Arch Comput Methods Eng 20:31–59
22.
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int J Numer Methods Eng 33(7):1331–1364CrossRefMathSciNetMATH
23.
Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int J Numer Methods Eng 33(7):1365–1382CrossRefMathSciNetMATH
24.
Kvamsdal T, Okstad KM (1998) Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int J Numer Methods Eng 42(3):443–472CrossRefMathSciNetMATH
25.
Wiberg NE, Abdulwahab F (1993) Patch recovery based on superconvergent derivatives and equilibrium. Int J Numer Methods Eng 36(16):2703–2724CrossRefMathSciNetMATH
26.
Wiberg NE, Abdulwahab F, Ziukas S (1994) Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. Int J Numer Methods Eng 37(20):3417–3440CrossRefMathSciNetMATH
27.
Blacker T, Belytschko T (1994) Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37(3):517–536CrossRefMathSciNetMATH
28.
Ródenas JJ, González-Estrada OA, Tarancón JE, Fuenmayor FJ (2008) A recovery-type error estimator for the extended finite element method based on singular+smooth stress field splitting. Int J Numer Methods Eng 76(4):545–571CrossRefMATH
29.
Ródenas JJ, González-Estrada OA, Díez P, Fuenmayor FJ (2010) Accurate recovery-based upper error bounds for the extended finite element framework. Comput Methods Appl Mech Eng 199(37–40):2607–2621CrossRefMATH
30.
Nadal E, (2014) Cartesian grid FEM (cgFEM): high performance h-adaptive FE analysis with efficient error control. Application to structural shape optimization. PhD thesis, Universitat Politècnica de València
31.
Karihaloo BL, Xiao QZ (2003) Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct 81(3):119–129CrossRef
32.
González-Estrada OA, Ródenas JJ, Chinesta F, Fuenmayor FJ (2013) Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM. Comput Mech 52:321–344CrossRefMathSciNetMATH
33.
Fuenmayor FJ, Oliver JL (1996) Criteria to achieve nearly optimal meshes in the h-adaptive finite element mehod. Int J Numer Methods Eng 39(23):4039–4061CrossRefMATH
34.
Fuenmayor F, Restrepo J, Tarancón J, Baeza L (2001) Error estimation and h-adaptive refinement in the analysis of natural frequencies. Finite Elem Anal Des 38:137–153CrossRefMATH
Metadaten
Titel
A separated representation of an error indicator for the mesh refinement process under the proper generalized decomposition framework
verfasst von
E. Nadal
A. Leygue
F. Chinesta
M. Beringhier
J. J. Ródenas
F. J. Fuenmayor
Publikationsdatum
01.02.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 2/2015
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-014-1097-y

Weitere Artikel der Ausgabe 2/2015

Computational Mechanics 2/2015 Zur Ausgabe

Erratum

Erratum to: Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration

Original Paper

An integrated method for the transient solution of reduced order models of geometrically nonlinear structures

Original Paper

A complementary study of analytical and computational fluid-structure interaction

Original Paper

A peridynamics–SPH coupling approach to simulate soil fragmentation induced by shock waves

Original Paper

A review on phase-field models of brittle fracture and a new fast hybrid formulation

Original Paper

Mesoscale modelling of crack-induced diffusivity in concrete

Neuer Inhalt

    Bildnachweise