메뉴 건너뛰기




Volumn 256, Issue , 2013, Pages 169-188

A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics

Author keywords

Domain decomposition; Model order reduction; Nonlinear fracture mechanics; Parametric time dependent problems; Proper orthogonal decomposition (POD); System approximation

Indexed keywords

DOMAIN DECOMPOSITIONS; MODEL ORDER REDUCTION; NONLINEAR FRACTURE MECHANICS; PROPER ORTHOGONAL DECOMPOSITIONS; SYSTEM APPROXIMATION; TIME-DEPENDENT PROBLEM;

EID: 84873277820     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.12.004     Document Type: Article
Times cited : (129)

References (64)
  • 2
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures. Part I: Coherent structures
    • Sirovich L. Turbulence and the dynamics of coherent structures. Part I: Coherent structures. Quarterly of Applied Mathematics 1987, 45:561-571.
    • (1987) Quarterly of Applied Mathematics , vol.45 , pp. 561-571
    • Sirovich, L.1
  • 3
    • 85128553849 scopus 로고    scopus 로고
    • A domain decomposition approach to pod, in: Proceedings of the 45th IEEE Conference on Decision and Control
    • C.A. Beattie, J. Borggaard, S. Gugercin, T. Iliescu, A domain decomposition approach to pod, in: Proceedings of the 45th IEEE Conference on Decision and Control, 2006.
    • (2006)
    • Beattie, C.A.1    Borggaard, J.2    Gugercin, S.3    Iliescu, T.4
  • 4
    • 47749108243 scopus 로고    scopus 로고
    • An interpolation method for adapting reduced-order models and application to aeroelasticity
    • Amsallem D., Farhat C. An interpolation method for adapting reduced-order models and application to aeroelasticity. AIAA Journal 2008, 46(7):1803-1813.
    • (2008) AIAA Journal , vol.46 , Issue.7 , pp. 1803-1813
    • Amsallem, D.1    Farhat, C.2
  • 6
    • 62549166192 scopus 로고    scopus 로고
    • Iterative methods for model reduction by domain decomposition
    • Buffoni M., Telib H., Iollo A. Iterative methods for model reduction by domain decomposition. Computers & Fluids 2009, 38(6):1160-1167.
    • (2009) Computers & Fluids , vol.38 , Issue.6 , pp. 1160-1167
    • Buffoni, M.1    Telib, H.2    Iollo, A.3
  • 8
    • 0031097279 scopus 로고    scopus 로고
    • A critique of mode acceleration and modal truncation augmentation methods for modal response analysis
    • Dickens J.M., Nakagawa J.M., Wittbrodt M.J. A critique of mode acceleration and modal truncation augmentation methods for modal response analysis. Computers and Structures 1997, 62(6):985-998.
    • (1997) Computers and Structures , vol.62 , Issue.6 , pp. 985-998
    • Dickens, J.M.1    Nakagawa, J.M.2    Wittbrodt, M.J.3
  • 9
    • 0037481177 scopus 로고    scopus 로고
    • Efficient model reduction in non-linear dynamics using the Karhunen-Loeve expansion and dual-weighted-residual methods
    • Meyer M., Matthies H.G. Efficient model reduction in non-linear dynamics using the Karhunen-Loeve expansion and dual-weighted-residual methods. Computational Mechanics 2003, 31(1):179-191.
    • (2003) Computational Mechanics , vol.31 , Issue.1 , pp. 179-191
    • Meyer, M.1    Matthies, H.G.2
  • 11
  • 13
    • 0002420869 scopus 로고
    • Vibrations of structural systems by component mode synthesis
    • Hurty W.C. Vibrations of structural systems by component mode synthesis. Journal of the Engineering Mechanics Division 1960, 86(4):51-70.
    • (1960) Journal of the Engineering Mechanics Division , vol.86 , Issue.4 , pp. 51-70
    • Hurty, W.C.1
  • 15
    • 15744385841 scopus 로고    scopus 로고
    • An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations
    • Barrault M., Maday Y., Nguyen N.C., Patera A.T. An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus de Mathématiques 2004, 339(9):667-672.
    • (2004) Comptes Rendus de Mathématiques , vol.339 , Issue.9 , pp. 667-672
    • Barrault, M.1    Maday, Y.2    Nguyen, N.C.3    Patera, A.T.4
  • 16
    • 84866431342 scopus 로고    scopus 로고
    • Residual minimizing model interpolation for parameterized nonlinear dynamical systems
    • Constantine P.G., Wang Q. Residual minimizing model interpolation for parameterized nonlinear dynamical systems. SIAM Journal on Scientific Computing 2012, 34:118-144.
    • (2012) SIAM Journal on Scientific Computing , vol.34 , pp. 118-144
    • Constantine, P.G.1    Wang, Q.2
  • 17
    • 0000325341 scopus 로고
    • On lines and planes of closest fit to systems of points in space
    • Pearson K. On lines and planes of closest fit to systems of points in space. Philosophical Magazine 1901, 2(6):559-572.
    • (1901) Philosophical Magazine , vol.2 , Issue.6 , pp. 559-572
    • Pearson, K.1
  • 18
    • 58149421595 scopus 로고
    • Analysis of a complex of statistical variables into principal components
    • Hotelling H. Analysis of a complex of statistical variables into principal components. Journal of Educational Psychology 1933, 24:417-441.
    • (1933) Journal of Educational Psychology , vol.24 , pp. 417-441
    • Hotelling, H.1
  • 20
    • 78650679450 scopus 로고    scopus 로고
    • Multi-level a priori hyper-reduction of mechanical models involving internal variables
    • Ryckelynck D., Benziane D.M. Multi-level a priori hyper-reduction of mechanical models involving internal variables. Computer Methods in Applied Mechanics and Engineering 2010, 199(17-20):1134-1142.
    • (2010) Computer Methods in Applied Mechanics and Engineering , vol.199 , Issue.17-20 , pp. 1134-1142
    • Ryckelynck, D.1    Benziane, D.M.2
  • 22
    • 78549239497 scopus 로고    scopus 로고
    • Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models
    • Chinesta F., Ammar A., Cueto E. Recent advances and new challenges in the use of the proper generalized decomposition for solving multidimensional models. Archives of Computational Methods in Engineering - State of the Art Reviews 2010, 17(4):327-350.
    • (2010) Archives of Computational Methods in Engineering - State of the Art Reviews , vol.17 , Issue.4 , pp. 327-350
    • Chinesta, F.1    Ammar, A.2    Cueto, E.3
  • 23
    • 77951238456 scopus 로고    scopus 로고
    • A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations
    • Nouy A. A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Computer Methods in Applied Mechanics and Engineering 2010, 199(23-24):1603-1626.
    • (2010) Computer Methods in Applied Mechanics and Engineering , vol.199 , Issue.23-24 , pp. 1603-1626
    • Nouy, A.1
  • 24
    • 33947145673 scopus 로고    scopus 로고
    • The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains
    • Yvonnet J., He Q.C. The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains. Journal of Computational Physics 2007, (1):341-368.
    • (2007) Journal of Computational Physics , Issue.1 , pp. 341-368
    • Yvonnet, J.1    He, Q.C.2
  • 25
    • 78650676597 scopus 로고    scopus 로고
    • Bridging proper orthogonal decomposition methods and augmented Newton-Krylov algorithms: an adaptive model order reduction for highly nonlinear mechanical problems
    • Kerfriden P., Gosselet P., Adhikari S., Bordas S. 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 2011, 200(5-8):850-866.
    • (2011) Computer Methods in Applied Mechanics and Engineering , vol.200 , Issue.5-8 , pp. 850-866
    • Kerfriden, P.1    Gosselet, P.2    Adhikari, S.3    Bordas, S.4
  • 27
    • 3042642522 scopus 로고    scopus 로고
    • Partitioned component mode synthesis via a flexibility approach
    • Park K.C., Park Y.H. Partitioned component mode synthesis via a flexibility approach. AIAA 2004, 42(5).
    • (2004) AIAA , vol.42 , Issue.5
    • Park, K.C.1    Park, Y.H.2
  • 28
    • 84873275098 scopus 로고    scopus 로고
    • Christian Rickelt, Stefanie Reese, A simulation strategy for life time calculations of large, partially damaged structures,
    • III European Conference on, Computational Mechanics
    • Christian Rickelt, Stefanie Reese, A simulation strategy for life time calculations of large, partially damaged structures, in: III European Conference on, Computational Mechanics, 2006.
    • (2006)
  • 30
    • 0031618714 scopus 로고    scopus 로고
    • Global/local analysis of composite plates with cracks
    • Haryadi S.G., Kapania R.K., Haryadi S.G. Global/local analysis of composite plates with cracks. Composites Part B 1998, 29(B):271-276.
    • (1998) Composites Part B , vol.29 B , pp. 271-276
    • Haryadi, S.G.1    Kapania, R.K.2    Haryadi, S.G.3
  • 31
    • 84873252556 scopus 로고    scopus 로고
    • Alonso Dynamic domain decomposition and error correction for reduced order models, in: AIAA 41st Aerospace Sciences Meeting
    • P.A. LeGresley, J.J. Alonso, Dynamic domain decomposition and error correction for reduced order models, in: AIAA 41st Aerospace Sciences Meeting, 2003.
    • (2003)
    • LeGresley, J.J.P.A.1
  • 33
    • 0038693394 scopus 로고    scopus 로고
    • Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics
    • Kunisch K., Volkwein S. Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM Journal on Numerical analysis 2003, 40(2):492-515.
    • (2003) SIAM Journal on Numerical analysis , vol.40 , Issue.2 , pp. 492-515
    • Kunisch, K.1    Volkwein, S.2
  • 36
    • 79952654642 scopus 로고    scopus 로고
    • Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
    • Carlberg K., Bou-Mosleh C., Farhat C. Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations. International Journal for Numerical Methods in Engineering 2011, 86(2):155-181.
    • (2011) International Journal for Numerical Methods in Engineering , vol.86 , Issue.2 , pp. 155-181
    • Carlberg, K.1    Bou-Mosleh, C.2    Farhat, C.3
  • 37
    • 0026239487 scopus 로고
    • A method of finite element tearing and interconnecting and its parallel solution algorithm
    • Farhat C., Roux F.X. A method of finite element tearing and interconnecting and its parallel solution algorithm. International Journal for Numerical Methods in Engineering 1991, 32:1205-1227.
    • (1991) International Journal for Numerical Methods in Engineering , vol.32 , pp. 1205-1227
    • Farhat, C.1    Roux, F.X.2
  • 39
    • 0028369940 scopus 로고
    • Domain decomposition methods in computational mechanics
    • Elsevier
    • Le Tallec P. Domain decomposition methods in computational mechanics. Computational Mechanics Advances 1994, vol. 1. Elsevier.
    • (1994) Computational Mechanics Advances , vol.1
    • Le Tallec, P.1
  • 42
    • 77956128819 scopus 로고    scopus 로고
    • On the control of the load increments for a proper description of multiple delamination in a domain decomposition framework
    • 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 2010, 10.1002/nme.2884.
    • (2010) International Journal for Numerical Methods in Engineering
    • Allix, O.1    Kerfriden, P.2    Gosselet, P.3
  • 45
    • 77951196297 scopus 로고    scopus 로고
    • A relocalization technique for the multiscale computation of delamination in composite structures
    • Allix O., Kerfriden P., Gosselet P. A relocalization technique for the multiscale computation of delamination in composite structures. Computer Modeling in Engineering and Sciences 2010, 55(3):271-291.
    • (2010) Computer Modeling in Engineering and Sciences , vol.55 , Issue.3 , pp. 271-291
    • Allix, O.1    Kerfriden, P.2    Gosselet, P.3
  • 46
    • 78549251697 scopus 로고    scopus 로고
    • Towards an adaptive POD/SVD surrogate model for aeronautic design
    • Jouhaud J.-C., Braconnier T., Ferrier M., Sagaut P. Towards an adaptive POD/SVD surrogate model for aeronautic design. Computers and Fluids 2011, 40(1):195-209.
    • (2011) Computers and Fluids , vol.40 , Issue.1 , pp. 195-209
    • Jouhaud, J.-C.1    Braconnier, T.2    Ferrier, M.3    Sagaut, P.4
  • 47
    • 84859959662 scopus 로고    scopus 로고
    • Certified reduced basis approximation for parametrized partial differential equations and applications
    • Quarteroni A., Rozza G., Manzoni A. Certified reduced basis approximation for parametrized partial differential equations and applications. Journal of Mathematics in Industry 2011, 1(3):1-44.
    • (2011) Journal of Mathematics in Industry , vol.1 , Issue.3 , pp. 1-44
    • Quarteroni, A.1    Rozza, G.2    Manzoni, A.3
  • 48
    • 6344220018 scopus 로고    scopus 로고
    • A quadratic method for nonlinear model order reduction
    • Proceeding of the International Conference on Modeling and Simulation of Microsystems
    • Y. Chen, J. White, A quadratic method for nonlinear model order reduction, in: Proceeding of the International Conference on Modeling and Simulation of Microsystems, 2000, pp. 470-480.
    • (2000) , pp. 470-480
    • Chen, Y.1    White, J.2
  • 49
    • 0037322638 scopus 로고    scopus 로고
    • A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices
    • Rewienski M., White J. A trajectory piecewise-linear approach to model order reduction and fast simulation of nonlinear circuits and micromachined devices. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 2003, 22(2):155-170.
    • (2003) IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems , vol.22 , Issue.2 , pp. 155-170
    • Rewienski, M.1    White, J.2
  • 52
    • 85088722743 scopus 로고    scopus 로고
    • Investigation of non-linear projection for POD based reduced order models for aerodynamics
    • LeGresley P.A., Alonso J.J. Investigation of non-linear projection for POD based reduced order models for aerodynamics. AIAA Paper 2001, 926:2001.
    • (2001) AIAA Paper , vol.926 , pp. 2001
    • LeGresley, P.A.1    Alonso, J.J.2
  • 53
    • 8744227253 scopus 로고    scopus 로고
    • A priori hyperreduction method: an adaptive approach
    • Ryckelynck D. A priori hyperreduction method: an adaptive approach. Journal of Computational Physics 2005, 202(1):346-366.
    • (2005) Journal of Computational Physics , vol.202 , Issue.1 , pp. 346-366
    • Ryckelynck, D.1
  • 54
    • 84873260146 scopus 로고    scopus 로고
    • Reduction of process simulation models - a proper orthogonal decomposition approach, Ph.D. report, Technical University of Eindhoven
    • P. Astrid, Reduction of process simulation models - a proper orthogonal decomposition approach, Ph.D. report, Technical University of Eindhoven, 2004.
    • (2004)
    • Astrid, P.1
  • 57
  • 58
    • 0000048673 scopus 로고
    • GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
    • Saad Y., Schultz M.H. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1986, 7(3):856-869.
    • (1986) SIAM Journal on Scientific and Statistical Computing , vol.7 , Issue.3 , pp. 856-869
    • Saad, Y.1    Schultz, M.H.2
  • 59
    • 0000005482 scopus 로고
    • BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems
    • Van der Vorst H.A. BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems. SIAM Journal on Scientific and Statistical Computing 1992, 13:631.
    • (1992) SIAM Journal on Scientific and Statistical Computing , vol.13 , pp. 631
    • Van der Vorst, H.A.1
  • 62
    • 0023526237 scopus 로고
    • Cross-validation in principal component analysis
    • Krzanowski W.J. Cross-validation in principal component analysis. Biometrics 1987, 43(3):575-584.
    • (1987) Biometrics , vol.43 , Issue.3 , pp. 575-584
    • Krzanowski, W.J.1
  • 63
    • 84873246518 scopus 로고    scopus 로고
    • Statistical extraction of process zones and representative subspaces in fracture of random composites, International Journal for Multiscale Computational Engineering Available from:
    • P. Kerfriden, K.M. Schmidt, T. Rabczuk, S.P.A. Bordas, Statistical extraction of process zones and representative subspaces in fracture of random composites, International Journal for Multiscale Computational Engineering (2012). Available from: arxiv:1203.2487v2.
    • (2012)
    • Kerfriden, P.1    Schmidt, K.M.2    Rabczuk, T.3    Bordas, S.P.A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.