메뉴 건너뛰기




Volumn 198, Issue 37-40, 2009, Pages 2839-2859

A short and versatile finite element multiscale code for homogenization problems

Author keywords

Composite material; FEM implementation; Macro to micro modeling; Microstructure; Multiscale method

Indexed keywords

COMPUTATIONAL STRATEGY; COUPLING CONDITION; FE METHOD; FEM IMPLEMENTATION; FINITE ELEMENT; HETEROGENEOUS MULTISCALE METHOD; HOMOGENIZATION PROBLEMS; MICROSIMULATION; MULTISCALE; MULTISCALE ALGORITHMS; MULTISCALE FINITE ELEMENT; MULTISCALE METHOD; NUMERICAL EXAMPLE; NUMERICAL INTEGRATIONS; PARABOLIC PROBLEMS; TIME-DEPENDENT PROBLEM;

EID: 68049087929     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.03.019     Document Type: Article
Times cited : (55)

References (34)
  • 1
    • 0036447606 scopus 로고    scopus 로고
    • Fourth order Chebyshev methods with recurrence relation
    • Abdulle A. Fourth order Chebyshev methods with recurrence relation. SIAM J. Sci. Comput. 23 (2002) 2042-2055
    • (2002) SIAM J. Sci. Comput. , vol.23 , pp. 2042-2055
    • Abdulle, A.1
  • 2
    • 17644387561 scopus 로고    scopus 로고
    • Heterogeneous multiscale FEM for diffusion problem on rough surfaces
    • Abdulle A., and Schwab C. Heterogeneous multiscale FEM for diffusion problem on rough surfaces. SIAM Multiscale Model. Simul. 3 1 (2005) 195-220
    • (2005) SIAM Multiscale Model. Simul. , vol.3 , Issue.1 , pp. 195-220
    • Abdulle, A.1    Schwab, C.2
  • 3
    • 33645988923 scopus 로고    scopus 로고
    • On a-priori error analysis of fully discrete heterogeneous multiscale FEM
    • Abdulle A. On a-priori error analysis of fully discrete heterogeneous multiscale FEM. SIAM Multiscale Model. Simul. 4 2 (2005) 447-459
    • (2005) SIAM Multiscale Model. Simul. , vol.4 , Issue.2 , pp. 447-459
    • Abdulle, A.1
  • 4
    • 33645990909 scopus 로고    scopus 로고
    • Analysis of a heterogeneous multiscale FEM for problems in elasticity
    • Abdulle A. Analysis of a heterogeneous multiscale FEM for problems in elasticity. Math. Mod. Meth. Appl. Sci. (M3AS) 16 2 (2006) 615-635
    • (2006) Math. Mod. Meth. Appl. Sci. (M3AS) , vol.16 , Issue.2 , pp. 615-635
    • Abdulle, A.1
  • 5
    • 68049111256 scopus 로고    scopus 로고
    • Heterogeneous Multiscale Methods with Quadrilateral Finite Elements
    • Springer, Berlin
    • Abdulle A. Heterogeneous Multiscale Methods with Quadrilateral Finite Elements. Numerical Mathematics and Advanced Applications (2006), Springer, Berlin 743-751
    • (2006) Numerical Mathematics and Advanced Applications , pp. 743-751
    • Abdulle, A.1
  • 6
    • 55249110253 scopus 로고    scopus 로고
    • Finite element heterogeneous multiscale methods with near optimal computational complexity
    • Abdulle A., and Engquist B. Finite element heterogeneous multiscale methods with near optimal computational complexity. SIAM Multiscale Model. Simul. 6 (2007) 1059-1084
    • (2007) SIAM Multiscale Model. Simul. , vol.6 , pp. 1059-1084
    • Abdulle, A.1    Engquist, B.2
  • 7
    • 38749152055 scopus 로고    scopus 로고
    • Multiscale method based on discontinuous finite element methods for homogenization problems
    • Abdulle A. Multiscale method based on discontinuous finite element methods for homogenization problems. C.R. Acad. Sci. Paris, Ser. I 346 (2007) 97-102
    • (2007) C.R. Acad. Sci. Paris, Ser. I , vol.346 , pp. 97-102
    • Abdulle, A.1
  • 8
    • 68049097915 scopus 로고    scopus 로고
    • The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs
    • Abdulle A. The finite element heterogeneous multiscale method: a computational strategy for multiscale PDEs. GAKUTO Int. Ser. Math. Sci. Appl. 31 (2009) 135-184
    • (2009) GAKUTO Int. Ser. Math. Sci. Appl. , vol.31 , pp. 135-184
    • Abdulle, A.1
  • 9
    • 0033469491 scopus 로고    scopus 로고
    • Remarks around 50 lines of Matlab: short finite element implementation
    • Alberty J., Carstensen C., and Funken S.A. Remarks around 50 lines of Matlab: short finite element implementation. Numer. Algorithms 20 2-3 (1999) 117-137
    • (1999) Numer. Algorithms , vol.20 , Issue.2-3 , pp. 117-137
    • Alberty, J.1    Carstensen, C.2    Funken, S.A.3
  • 11
    • 79956016800 scopus 로고    scopus 로고
    • Carbon nanotube composites for thermal management
    • Biercuk J., et al. Carbon nanotube composites for thermal management. Appl. Phys. Lett., AIP 80 15 (2002) 2767
    • (2002) Appl. Phys. Lett., AIP , vol.80 , Issue.15 , pp. 2767
    • Biercuk, J.1
  • 14
    • 68049103939 scopus 로고    scopus 로고
    • .
  • 16
    • 0035088146 scopus 로고    scopus 로고
    • An approach to micro-macro modeling of heterogeneous materials
    • Kouznetsova V., Brekelmans W.A.M., and Baaijens F.P.T. An approach to micro-macro modeling of heterogeneous materials. Comput. Mech. 27 (2001) 37-48
    • (2001) Comput. Mech. , vol.27 , pp. 37-48
    • Kouznetsova, V.1    Brekelmans, W.A.M.2    Baaijens, F.P.T.3
  • 17
    • 8644290775 scopus 로고    scopus 로고
    • Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy
    • Kouznetsova V., Geers M., and Brekelmans W. Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy. Comput. Methods Appl. Mech. Engrg. 193 (2004) 5525-5550
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , pp. 5525-5550
    • Kouznetsova, V.1    Geers, M.2    Brekelmans, W.3
  • 18
    • 85128805678 scopus 로고    scopus 로고
    • The heterogeneous multi-scale methods
    • Engquist B. The heterogeneous multi-scale methods. Commun. Math. Sci. 1 1 (2003) 87-132
    • (2003) Commun. Math. Sci. , vol.1 , Issue.1 , pp. 87-132
    • Engquist, B.1
  • 19
    • 13644268174 scopus 로고    scopus 로고
    • Analysis of the heterogeneous multiscale method for elliptic homogenization problems
    • Ming P., and Zhang P. Analysis of the heterogeneous multiscale method for elliptic homogenization problems. J. AMS 18 1 (2004) 121-156
    • (2004) J. AMS , vol.18 , Issue.1 , pp. 121-156
    • Ming, P.1    Zhang, P.2
  • 21
    • 0029368201 scopus 로고
    • Multigrid method for periodic heterogeneous media. I. Convergence studies for one-dimensional case
    • Fish J., and Belsky V. Multigrid method for periodic heterogeneous media. I. Convergence studies for one-dimensional case. Comput. Methods Appl. Mech. Engrg. 126 (1995) 1-16
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.126 , pp. 1-16
    • Fish, J.1    Belsky, V.2
  • 22
    • 0029371171 scopus 로고
    • Multigrid method for periodic heterogeneous media. II. Multiscale modeling and quality control in multidimensional case
    • Fish J., and Belsky V. Multigrid method for periodic heterogeneous media. II. Multiscale modeling and quality control in multidimensional case. Comput. Methods Appl. Mech. Engrg. 126 (1995) 17-38
    • (1995) Comput. Methods Appl. Mech. Engrg. , vol.126 , pp. 17-38
    • Fish, J.1    Belsky, V.2
  • 23
    • 17644363709 scopus 로고    scopus 로고
    • High-dimensional finite elements for elliptic problems with multiple scales
    • Hoang V.H., and Schwab C. High-dimensional finite elements for elliptic problems with multiple scales. SIAM Multiscale Model. Simulat. 3 1 (2005) 195-220
    • (2005) SIAM Multiscale Model. Simulat. , vol.3 , Issue.1 , pp. 195-220
    • Hoang, V.H.1    Schwab, C.2
  • 24
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou T., and Wu X. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput Phys. 134 (1997) 169-189
    • (1997) J. Comput Phys. , vol.134 , pp. 169-189
    • Hou, T.1    Wu, X.2
  • 25
    • 68049107057 scopus 로고    scopus 로고
    • V. Kippe, J.E. Aarnes, K.-A. Lie, A comparison of multiscale methods for elliptic problems in porous media flow, Comput. Geosci., 2007, (Special issue on multiscale methods).
    • V. Kippe, J.E. Aarnes, K.-A. Lie, A comparison of multiscale methods for elliptic problems in porous media flow, Comput. Geosci., 2007, (Special issue on multiscale methods).
  • 26
    • 0037474370 scopus 로고    scopus 로고
    • Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy
    • Miehe C. Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy. Comput. Methods Appl. Mech. Engrg. 192 (2003) 559-591
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 559-591
    • Miehe, C.1
  • 27
    • 33644559401 scopus 로고    scopus 로고
    • Numerical methods for multiscale elliptic problems
    • Ming P., and Yue Y. Numerical methods for multiscale elliptic problems. J. Comput. Phys. 214 1 (2006) 421-445
    • (2006) J. Comput. Phys. , vol.214 , Issue.1 , pp. 421-445
    • Ming, P.1    Yue, Y.2
  • 28
    • 34249311837 scopus 로고    scopus 로고
    • Multiscale modeling of physical phenomena: adaptive control of models
    • Oden J.T., Prudhomme S., Romkes A., and Bauman P. Multiscale modeling of physical phenomena: adaptive control of models. SIAM J. Sci. Comput. 28 (2006) 2359-2389
    • (2006) SIAM J. Sci. Comput. , vol.28 , pp. 2359-2389
    • Oden, J.T.1    Prudhomme, S.2    Romkes, A.3    Bauman, P.4
  • 29
    • 0036659380 scopus 로고    scopus 로고
    • Two-scale FEM for homogenization problems
    • Matache A.M., and Schwab C. Two-scale FEM for homogenization problems. R.A.I.R.O. Anal. Numer. 36 (2002) 537-572
    • (2002) R.A.I.R.O. Anal. Numer. , vol.36 , pp. 537-572
    • Matache, A.M.1    Schwab, C.2
  • 31
    • 0035919604 scopus 로고    scopus 로고
    • A class of general algorithm for multi-scale analyses of heterogeneous media
    • Terada K., and Kikuchi N. A class of general algorithm for multi-scale analyses of heterogeneous media. Comput. Methods Appl. Mech. Engrg. 190 (2001) 5427-5464
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 5427-5464
    • Terada, K.1    Kikuchi, N.2
  • 32
    • 0032836187 scopus 로고    scopus 로고
    • Accurate scale up of two phase flow using renormalization and nonuniform coarsening
    • Wallstrom T.C., Hou S., Christie M.A., Durlofsky L.J., and Sharp D.H. Accurate scale up of two phase flow using renormalization and nonuniform coarsening. Comput. Geosci. 3 1 (1999) 67-87
    • (1999) Comput. Geosci. , vol.3 , Issue.1 , pp. 67-87
    • Wallstrom, T.C.1    Hou, S.2    Christie, M.A.3    Durlofsky, L.J.4    Sharp, D.H.5
  • 33
    • 33847119952 scopus 로고    scopus 로고
    • The local microscale problem in the multiscale modeling of strongly heterogeneous media: effects of boundary conditions and cell size
    • Yue Y., and E W. The local microscale problem in the multiscale modeling of strongly heterogeneous media: effects of boundary conditions and cell size. J. Comput. Phys. 222 2 (2006) 556-572
    • (2006) J. Comput. Phys. , vol.222 , Issue.2 , pp. 556-572
    • Yue, Y.1
  • 34
    • 0032099439 scopus 로고    scopus 로고
    • C. Zweben, Advances in composite materials for thermal management in electronic packaging, in: JOM Journal of the Minerals, Metals and Materials Society, 50, 1998, Springer, pp. 47-51.
    • C. Zweben, Advances in composite materials for thermal management in electronic packaging, in: JOM Journal of the Minerals, Metals and Materials Society, vol. 50, 1998, Springer, pp. 47-51.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.