메뉴 건너뛰기




Volumn 34, Issue 2, 2012, Pages

A quasi-algebraic multigrid approach to fracture problems based on extended finite elements

Author keywords

Algebraic multigrid; Extended finite elements; Fracture; Iterative methods

Indexed keywords

ALGEBRA; CRACKS; FINITE ELEMENT METHOD; FRACTURE; LINEAR SYSTEMS; NUMERICAL METHODS;

EID: 84861375720     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/110819913     Document Type: Article
Times cited : (35)

References (36)
  • 2
    • 67650733836 scopus 로고    scopus 로고
    • A review of extended/generalized finite element models for material modeling
    • Birkhaüser, Basel
    • T. Belytschko, R. Gracie, and G. Ventura, A Review of Extended/Generalized Finite Element Models for Material Modeling, Model. Simul. Materials Sci. Engrg. 17, Birkhaüser, Basel, 2009, pp. 1-24.
    • (2009) Model. Simul. Materials Sci. Engrg. , vol.17 , pp. 1-24
    • Belytschko, T.1    Gracie, R.2    Ventura, G.3
  • 3
    • 84858341078 scopus 로고    scopus 로고
    • Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods
    • also available online from
    • L. Berger-Vergiat, H. Waisman, B. Hiriyur, R. Tuminaro, and D. Keyes, Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods, Internat. J. Numer. Methods Engrg., (2011); also available online from http://dx.doi.org/10.1002/nme.3318.
    • (2011) Internat. J. Numer. Methods Engrg.
    • Berger-Vergiat, L.1    Waisman, H.2    Hiriyur, B.3    Tuminaro, R.4    Keyes, D.5
  • 6
    • 0142096515 scopus 로고    scopus 로고
    • Multiscale scientific computation: Review 2001
    • Springer-Verlag, Berlin
    • A. Brandt, Multiscale scientific computation: Review 2001, in Multiscale Multiresolution Methods, Springer-Verlag, Berlin, 2001, pp. 1-96.
    • (2001) Multiscale Multiresolution Methods , pp. 1-96
    • Brandt, A.1
  • 7
    • 84878786891 scopus 로고    scopus 로고
    • Algebraic multigrid methods based on compatible relaxation and energy minimization
    • O.Widlund and D. E. Keyes, eds., Lecture Notes in Comput. Sci. Engrg., Springer-Verlag, Berlin
    • J. Brannick and L. Zikatanov, Algebraic multigrid methods based on compatible relaxation and energy minimization, in Domain Decomposition Methods in Science and Engineering XVI, O.Widlund and D. E. Keyes, eds., Lecture Notes in Comput. Sci. Engrg. 55, Springer- Verlag, Berlin, 2007, pp. 15-26.
    • (2007) Domain Decomposition Methods in Science and Engineering XVI , vol.55 , pp. 15-26
    • Brannick, J.1    Zikatanov, L.2
  • 9
    • 85140870810 scopus 로고    scopus 로고
    • Algebraic two-level preconditioners for the Schur complement method
    • L. M. Carvalho, L. Giraud, and P. L. Tallec, Algebraic two-level preconditioners for the Schur complement method, SIAM J. Sci. Comput., 22 (1998), pp. 200-1.
    • (1998) SIAM J. Sci. Comput. , vol.22 , pp. 200-201
    • Carvalho, L.M.1    Giraud, L.2    Tallec, P.L.3
  • 10
    • 36749016215 scopus 로고    scopus 로고
    • A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes
    • DOI 10.1515/jnma.2007.008
    • D. Cho and L. Zikatanov, A multilevel preconditioning for generalized finite element method problems on unstructured simplicial meshes, J. Numer. Math., 15 (2007), pp. 163-180. (Pubitemid 350216002)
    • (2007) Journal of Numerical Mathematics , vol.15 , Issue.3 , pp. 163-180
    • Cho, D.1    Zikatanov, L.2
  • 13
    • 0001253456 scopus 로고
    • A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation
    • D. Keyes andW. Gropp, A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation, SIAM J. Sci. Statist. Comput., 8 (1987), pp. s166-s202.
    • (1987) SIAM J. Sci. Statist. Comput. , vol.8
    • Keyes, D.1    Gropp, W.2
  • 14
    • 33750744063 scopus 로고    scopus 로고
    • AMG by element agglomeration and constrained energy minimization interpolation
    • DOI 10.1002/nla.494
    • T. V. Kolev and P. S. Vassilevski, AMG by element agglomeration and constrained energy minimization interpolation, Numer. Linear Algebra Appl., 13 (2006), pp. 771-788. (Pubitemid 44703451)
    • (2006) Numerical Linear Algebra with Applications , vol.13 , Issue.9 , pp. 771-788
    • Kolev, T.V.1    Vassilevski, P.S.2
  • 16
    • 0032634013 scopus 로고    scopus 로고
    • Energy optimization of algebraic multigrid bases
    • J. Mandel, M. Brezina, and P. Vaněk, Energy optimization of algebraic multigrid bases, Computing, 62 (1999), pp. 205-228.
    • (1999) Computing , vol.62 , pp. 205-228
    • Mandel, J.1    Brezina, M.2    Vaněk, P.3
  • 17
    • 0002963824 scopus 로고
    • Multigrid methods for variational problems
    • S. McCormick and J. Ruge, Multigrid methods for variational problems, SIAM J. Numer. Anal., 19 (1982), pp. 924-929.
    • (1982) SIAM J. Numer. Anal. , vol.19 , pp. 924-929
    • McCormick, S.1    Ruge, J.2
  • 18
    • 0030380578 scopus 로고    scopus 로고
    • The partition of unity finite element method: Basic theory and applications
    • PII S0045782596010870
    • J. M. Melenk and I. Babuška, The partition of unity finite element method: Basic theory and applications, Comput. Methods Appl. Mech. Engrg., 139 (1996), pp. 289-314. (Pubitemid 126382701)
    • (1996) Computer Methods in Applied Mechanics and Engineering , vol.139 , Issue.1-4 , pp. 289-314
    • Melenk, J.M.1    Babuska, I.2
  • 19
    • 79951933574 scopus 로고    scopus 로고
    • A robust preconditioning technique for the extended finite element method
    • A. Menk and S. Bordas, A robust preconditioning technique for the extended finite element method, Internat. J. Numer. Methods Engrg., 85 (2011), pp. 1609-1632.
    • (2011) Internat. J. Numer. Methods Engrg. , vol.85 , pp. 1609-1632
    • Menk, A.1    Bordas, S.2
  • 22
    • 79957601089 scopus 로고    scopus 로고
    • A general interpolation strategy for algebraic multigrid using energy minimization
    • L. N. Olson, J. Schroder, and R. S. Tuminaro, A general interpolation strategy for algebraic multigrid using energy minimization, J. Comput. Phys., 33 (2011), pp. 966-991.
    • (2011) J. Comput. Phys. , vol.33 , pp. 966-991
    • Olson, L.N.1    Schroder, J.2    Tuminaro, R.S.3
  • 23
    • 60949107076 scopus 로고    scopus 로고
    • A multigrid extended finite element method for elastic crack growth simulation
    • J. Rannou, A. Gravouil, and A. Combescure, A multigrid extended finite element method for elastic crack growth simulation, Eur. J. Comp. Mech., 16 (2007), pp. 161-182.
    • (2007) Eur. J. Comp. Mech. , vol.16 , pp. 161-182
    • Rannou, J.1    Gravouil, A.2    Combescure, A.3
  • 24
    • 77956173968 scopus 로고    scopus 로고
    • Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions
    • J. Shi, D. Chopp, J. Lua, N. Sukumar, and T. Belytschko, Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions, Engrg. Fracture Mech., 77 (2010), pp. 2840-2863.
    • (2010) Engrg. Fracture Mech. , vol.77 , pp. 2840-2863
    • Shi, J.1    Chopp, D.2    Lua, J.3    Sukumar, N.4    Belytschko, T.5
  • 28
    • 2942526684 scopus 로고    scopus 로고
    • Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines
    • J. Donnelley, ed.
    • R. Tuminaro and C. Tong, Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines, in SuperComputing 2000 Proceedings, J. Donnelley, ed., 2000.
    • (2000) SuperComputing 2000 Proceedings
    • Tuminaro, R.1    Tong, C.2
  • 29
    • 0041034172 scopus 로고    scopus 로고
    • Convergence of algebraic multigrid based on smoothed aggregation
    • DOI 10.1007/s211-001-8015-y
    • P. Vaněk, M. Brezina, and J. Mandel, Convergence of algebraic multigrid based on smoothed aggregation, Numer. Math., 88 (2001), pp. 559-579. (Pubitemid 33573395)
    • (2001) Numerische Mathematik , vol.88 , Issue.3 , pp. 559-579
    • Vanek, P.1    Brezina, M.2    Mandel, J.3
  • 30
    • 0030388574 scopus 로고    scopus 로고
    • Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems
    • P. Vaněk, J. Mandel, and M. Brezina, Algebraic multigrid based on smoothed aggregation for second and fourth order problems, Computing, 56 (1996), pp. 179-196. (Pubitemid 126633416)
    • (1996) Computing (Vienna/New York) , vol.56 , Issue.3 , pp. 179-196
    • Vanek, P.1    Mandel, J.2    Brezina, M.3
  • 31
    • 77249093542 scopus 로고    scopus 로고
    • General constrained energy minimization interpolation mappings for AMG
    • P. S. Vassilevski, General constrained energy minimization interpolation mappings for AMG, SIAM J. Sci. Comput., 32 (2010), pp. 1-13.
    • (2010) SIAM J. Sci. Comput. , vol.32 , pp. 1-13
    • Vassilevski, P.S.1
  • 32
    • 0000012023 scopus 로고    scopus 로고
    • On the algebraic construction of multilevel transfer operators
    • C. Wagner, On the algebraic construction of multilevel transfer operators, Computing, 65 (2000), pp. 73-95.
    • (2000) Computing , vol.65 , pp. 73-95
    • Wagner, C.1
  • 33
    • 0033293066 scopus 로고    scopus 로고
    • An energy-minimizing interpolation for robust multigrid methods
    • W. L. Wan, T. F. Chan, and B. Smith, An energy-minimizing interpolation for robust multigrid methods, SIAM J. Sci. Comput., 21 (2000), pp. 1632-1649.
    • (2000) SIAM J. Sci. Comput. , vol.21 , pp. 1632-1649
    • Wan, W.L.1    Chan, T.F.2    Smith, B.3
  • 35
    • 33750160340 scopus 로고    scopus 로고
    • On an energy minimizing basis for algebraic multigrid methods
    • J. Xu and L. Zikatanov, On an energy minimizing basis for algebraic multigrid methods, Comput. Vis. Sci., 7 (2004), pp. 121-127(7).
    • (2004) Comput. Vis. Sci. , vol.7 , pp. 121-1277
    • Xu, J.1    Zikatanov, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.