메뉴 건너뛰기




Volumn 31, Issue 2, 2008, Pages 1399-1423

A nonsmooth multiscale method for solving frictional two-body contact problems in 2d and 3d with multigrid efficiency

Author keywords

Contact problems; Friction; Multibody contact; Multigrid methods; Nonconforming domain decomposition

Indexed keywords

ALGEBRA; DOMAIN DECOMPOSITION METHODS; EFFICIENCY; ITERATIVE METHODS; NUMERICAL METHODS; PROBLEM SOLVING; TRIBOLOGY;

EID: 64049114843     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/070682514     Document Type: Article
Times cited : (46)

References (40)
  • 3
    • 0000236329 scopus 로고    scopus 로고
    • Approximation of the unilateral contact problem by the mortar finite element method
    • F. BEN BELGACEM, P. HILD, AND P. lABORDE, Approximation of the unilateral contact problem by the mortar finite element method, C. R. Acad. Sci., Paris, Ser. I, 324 (1997), pp. 123-127.
    • (1997) C. R. Acad. Sci., Paris, Ser. I , vol.324 , pp. 123-127
    • BEN BELGACEM, F.1    HILD, P.2    lABORDE, P.3
  • 4
    • 67649486407 scopus 로고    scopus 로고
    • C. BERNARDI, Y. MADAY, AND A. PATERA, Domain decomposition by the mortar element method, in Asymptotic and numerical methods for partial differential equations with critical parameters, H. K. et al., ed., Reidel, Dordrecht, 1993, pp. 269-286.
    • C. BERNARDI, Y. MADAY, AND A. PATERA, Domain decomposition by the mortar element method, in Asymptotic and numerical methods for partial differential equations with critical parameters, H. K. et al., ed., Reidel, Dordrecht, 1993, pp. 269-286.
  • 5
    • 0033295419 scopus 로고    scopus 로고
    • Adaptive finite elements for elastic bodies in contact
    • C. CARSTENSEN, O. SCHERF, AND P. wRIGGERS, Adaptive finite elements for elastic bodies in contact, SIAM J. Sci. Comput., 20 (1999), pp. 1605-1626.
    • (1999) SIAM J. Sci. Comput , vol.20 , pp. 1605-1626
    • CARSTENSEN, C.1    SCHERF, O.2    wRIGGERS, P.3
  • 7
    • 0010854270 scopus 로고
    • Internal approximation of quasi-variational inequalities,Nu- mer
    • A. R. CǍPǍ̧INǍ AND M. COCU, Internal approximation of quasi-variational inequalities,Nu- mer. Math., 59 (1991), pp. 385-398.
    • (1991) Math , vol.59 , pp. 385-398
    • CǍPǍ̧INǍ, A.R.1    COCU, M.2
  • 8
    • 67649483888 scopus 로고    scopus 로고
    • T. DICKOPF AND R. KRAUSE, Efficient simulation of multi-body contact problems on complex geometries: A flexible dcomposition approach using constrained minimization,\NS- preprint 711, Institute for Numerical Simulation, University of Bonn, March 2008.
    • T. DICKOPF AND R. KRAUSE, Efficient simulation of multi-body contact problems on complex geometries: A flexible dcomposition approach using constrained minimization,\NS- preprint 711, Institute for Numerical Simulation, University of Bonn, March 2008.
  • 9
    • 0036502746 scopus 로고    scopus 로고
    • Implementation of the fixed point method in contact problems with Coulomb friction based on a dual splitting type technique
    • Z. DOSTAL, J. hASLINGER, AND R. KUČERA, Implementation of the fixed point method in contact problems with Coulomb friction based on a dual splitting type technique,J. Comp. Appl. Math., 140 (2002), pp. 245-256.
    • (2002) J. Comp. Appl. Math , vol.140 , pp. 245-256
    • DOSTAL, Z.1    hASLINGER, J.2    KUČERA, R.3
  • 10
    • 0001190362 scopus 로고    scopus 로고
    • Duality based solution of contact problem with Coulomb friction
    • Z. DOSTAL AND V. V.ÓNDRAK, Duality based solution of contact problem with Coulomb friction, Arch. Mech., 49 (1997), pp. 453-460.
    • (1997) Arch. Mech , vol.49 , pp. 453-460
    • DOSTAL, Z.1    V.ÓNDRAK, V.2
  • 14
    • 0021603638 scopus 로고
    • Numerical methods for nonlinear variational problems
    • Springer, New York
    • R. GLOWINSKI, Numerical methods for nonlinear variational problems, Series in Computational Physics, Springer, New York, 1984.
    • (1984) Series in Computational Physics
    • GLOWINSKI, R.1
  • 16
    • 67649505738 scopus 로고    scopus 로고
    • S. GRATTON, A. SARTENAER, AND P. tOINT, Recursive trust-region methods for multiscale nonlinear optimization, CERFACS, 06 (2006).
    • S. GRATTON, A. SARTENAER, AND P. tOINT, Recursive trust-region methods for multiscale nonlinear optimization, CERFACS, 06 (2006).
  • 17
    • 0020887530 scopus 로고
    • Approximation of the Signorini problem with friction, obeying the Coulomb law
    • J. HASLINGER, Approximation of the Signorini problem with friction, obeying the Coulomb law, Math. Methods Appl. Sci, 5 (1983), pp. 422-437.
    • (1983) Math. Methods Appl. Sci , vol.5 , pp. 422-437
    • HASLINGER, J.1
  • 18
    • 0033895887 scopus 로고    scopus 로고
    • Numerical implementation of two nonconforming finite element methods for unilateral contact
    • P. HILD, Numerical implementation of two nonconforming finite element methods for unilateral contact, Comput. Methods Appl. Mech. Engrg., 184 (2000), pp. 99-123.
    • (2000) Comput. Methods Appl. Mech. Engrg , vol.184 , pp. 99-123
    • HILD, P.1
  • 19
    • 0042640863 scopus 로고    scopus 로고
    • On finite element uniqueness studies for Coulomb's frictional contact model,Int.J
    • P. HILD, On finite element uniqueness studies for Coulomb's frictional contact model,Int.J. Appl. Math. Comput. Sci., 12 (2002), pp. 41-50.
    • (2002) Appl. Math. Comput. Sci , vol.12 , pp. 41-50
    • HILD, P.1
  • 20
    • 0041657515 scopus 로고    scopus 로고
    • The primal dual active set strategy as a semis- mooth newton method
    • M. HINTERMÜLLER, K. ITO, AND K. KUNISCH, The primal dual active set strategy as a semis- mooth newton method, SIAM J. Optim., 13 (2003), pp. 865-888.
    • (2003) SIAM J. Optim , vol.13 , pp. 865-888
    • HINTERMÜLLER, M.1    ITO, K.2    KUNISCH, K.3
  • 22
    • 33644559359 scopus 로고    scopus 로고
    • An optimal a priori error estimate for non-linear multibody contact problems
    • S. HÜEBER AND B. WOHLMUTH, An optimal a priori error estimate for non-linear multibody contact problems, SIAM J. Numer. Anal., 43 (2005), pp. 156-173.
    • (2005) SIAM J. Numer. Anal , vol.43 , pp. 156-173
    • HÜEBER, S.1    WOHLMUTH, B.2
  • 23
    • 67649487439 scopus 로고    scopus 로고
    • J. JARUŠEK, Contact problems with bounded friction. Coercive case, Czechoslovak Math. J., 33 (1983), pp. 237-261.
    • J. JARUŠEK, Contact problems with bounded friction. Coercive case, Czechoslovak Math. J., 33 (1983), pp. 237-261.
  • 26
    • 0036627648 scopus 로고    scopus 로고
    • On constrained Newton linearization and multigrid for variational inequalities
    • R. KORNHUBER, On constrained Newton linearization and multigrid for variational inequalities, Numer. Math., 91 (2002), pp. 699-721.
    • (2002) Numer. Math , vol.91 , pp. 699-721
    • KORNHUBER, R.1
  • 27
    • 0242507151 scopus 로고    scopus 로고
    • Adaptive multigrid methods for Signorini's problem in linear elasticity
    • R. KORNHUBER AND R. KRAUSE, Adaptive multigrid methods for Signorini's problem in linear elasticity, Comput. Vis. Sci., 4 (2001), pp. 699-721.
    • (2001) Comput. Vis. Sci , vol.4 , pp. 699-721
    • KORNHUBER, R.1    KRAUSE, R.2
  • 28
    • 33746103660 scopus 로고    scopus 로고
    • Robust multigrid methods for vector-valued Allen-Cahn equations with logarithmic free energy
    • R. KORNHUBER AND R. KRAUSE, Robust multigrid methods for vector-valued Allen-Cahn equations with logarithmic free energy, Comput. Vis. Sci., 9 (2006), pp. 103-116.
    • (2006) Comput. Vis. Sci , vol.9 , pp. 103-116
    • KORNHUBER, R.1    KRAUSE, R.2
  • 30
    • 33749023343 scopus 로고    scopus 로고
    • From inexact active set strategies to nonlinear multigrid methods
    • Analysis and Simulation of Contact Problems, P. Wriggers and U. Nackenhorst, eds, Springer, New York
    • R. KRAUSE, From inexact active set strategies to nonlinear multigrid methods, in Analysis and Simulation of Contact Problems, P. Wriggers and U. Nackenhorst, eds., Lecture Notes in Applied and Computational Mechanics 27, Springer, New York, 2006.
    • (2006) Lecture Notes in Applied and Computational Mechanics , vol.27
    • KRAUSE, R.1
  • 31
    • 84880382016 scopus 로고    scopus 로고
    • Fast solving of contact problems on complicated geometries
    • Domain Decomposition Methods in Science and Engineering, R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Widlund, and J. Xu, eds, Springer, New York
    • R. KRAUSE AND O. SANDER, Fast solving of contact problems on complicated geometries,in Domain Decomposition Methods in Science and Engineering, R. Kornhuber, R. Hoppe, J. Périaux, O. Pironneau, O. Widlund, and J. Xu, eds., Lecture Notes in Computational Science and Engineering 40, Springer, New York, 2005.
    • (2005) Lecture Notes in Computational Science and Engineering , vol.40
    • KRAUSE, R.1    SANDER, O.2
  • 32
    • 25444494721 scopus 로고    scopus 로고
    • Generalized Newton methods for the 2d-Signorini contact problem with friction in function space
    • K. KUNISCH AND G. STADLER, Generalized Newton methods for the 2d-Signorini contact problem with friction in function space, M2AN, (2005), pp. 827-854.
    • (2005) M2AN , pp. 827-854
    • KUNISCH, K.1    STADLER, G.2
  • 33
    • 39449138069 scopus 로고    scopus 로고
    • Fixed point strategies for elastostatic frictional contact problems
    • P. LABORDE AND Y. RENARD, Fixed point strategies for elastostatic frictional contact problems, Math. Methods Appl. Sci., 31 (2003), pp. 415-441.
    • (2003) Math. Methods Appl. Sci , vol.31 , pp. 415-441
    • LABORDE, P.1    RENARD, Y.2
  • 34
    • 67649504924 scopus 로고    scopus 로고
    • C. LICHT, E. PRATT, AND M. RAOUS, Remarks on a numerical method for unilateral contact including friction, in Unilateral Problems in Structural Analysis IV, F. M. G. del Piero, ed., International Series of Numerical Mathematics, Basel, 1991, Birkhauser, pp. 129-144.
    • C. LICHT, E. PRATT, AND M. RAOUS, Remarks on a numerical method for unilateral contact including friction, in Unilateral Problems in Structural Analysis IV, F. M. G. del Piero, ed., International Series of Numerical Mathematics, Basel, 1991, Birkhauser, pp. 129-144.
  • 35
    • 0000328269 scopus 로고
    • On the solution of the variational inequality to the Signorini problem with small friction
    • J. NEČAS, J. JARUŠEK, AND J. HASLINGER, On the solution of the variational inequality to the Signorini problem with small friction, Boll. Unione Mat. Ital., 17 (1980), pp. 796-811.
    • (1980) Boll. Unione Mat. Ital , vol.17 , pp. 796-811
    • NEČAS, J.1    JARUŠEK, J.2    HASLINGER, J.3
  • 36
    • 0442328968 scopus 로고    scopus 로고
    • A mortar segment-to-segment contact method for large deformation solid mechanics
    • M. PUSO AND T. LAURSEN, A mortar segment-to-segment contact method for large deformation solid mechanics, J. Comp. Meth. Appl. Mech. Engrg., 193 (2004), pp. 601-629.
    • (2004) J. Comp. Meth. Appl. Mech. Engrg , vol.193 , pp. 601-629
    • PUSO, M.1    LAURSEN, T.2
  • 37
    • 1642370513 scopus 로고    scopus 로고
    • Solving unsymmetric sparse systems of linear equations with PARDISO
    • O. SCHENK AND K. GÄURTNER, Solving unsymmetric sparse systems of linear equations with PARDISO, J. Future Generation Comput. Systems, 20 (2004), pp. 475-487.
    • (2004) J. Future Generation Comput. Systems , vol.20 , pp. 475-487
    • SCHENK, O.1    GÄURTNER, K.2
  • 38
    • 0036003411 scopus 로고    scopus 로고
    • Global and uniform convergence of subspace correction methods for some convex optimization problems
    • X.-C. TAI AND J. XU, Global and uniform convergence of subspace correction methods for some convex optimization problems, Math. Comput., 71 (2002), pp. 105-124.
    • (2002) Math. Comput , vol.71 , pp. 105-124
    • TAI, X.-C.1    XU, J.2
  • 39
    • 0034437154 scopus 로고    scopus 로고
    • A mortar finite element method using dual spaces for the Lagrange multiplier
    • B. WOHLMUTH, A mortar finite element method using dual spaces for the Lagrange multiplier, SIAM J. Numer. Anal., 38 (2000), pp. 989-1012.
    • (2000) SIAM J. Numer. Anal , vol.38 , pp. 989-1012
    • WOHLMUTH, B.1
  • 40
    • 1842564097 scopus 로고    scopus 로고
    • Monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems
    • B. WOHLMUTH AND R. KRAUSE, Monotone multigrid methods on nonmatching grids for nonlinear multibody contact problems, SIAM J. Sci. Comput., 25 (2003), pp. 324-347.
    • (2003) SIAM J. Sci. Comput , vol.25 , pp. 324-347
    • WOHLMUTH, B.1    KRAUSE, R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.