Free Access
Issue
ESAIM: M2AN
Volume 45, Number 3, May-June 2011
Page(s) 563 - 602
DOI https://doi.org/10.1051/m2an/2010067
Published online 30 November 2010
  1. S. Balay, W.D. Gropp, L.C. McInnes and B.F. Smith, Efficient management of parallelism in object oriented numerical software libraries, in Modern Software Tools in Scientific Computing, E. Arge, A.M. Bruaset and H.P. Langtangen Eds., Birkhäuser Press (1997) 163–202. [Google Scholar]
  2. S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M. Knepley, L.C. McInnes, B.F. Smith and H. Zhang, PETSc users manual. Technical Report ANL-95/11 – Revision 2.2.3, Argonne National Laboratory (2007). [Google Scholar]
  3. S. Balay, K. Buschelman, W.D. Gropp, D. Kaushik, M.G. Knepley, L.C. McInnes, B.F. Smith and H. Zhang, PETSc Web page, http://www.mcs.anl.gov/petsc (2009). [Google Scholar]
  4. J.M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics, in Herriot Watt Symposion: Nonlinear Analysis and Mechanics 1, R.J. Knops Ed., Pitman, London (1977) 187–238. [Google Scholar]
  5. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rat. Mech. Anal. 63 (1977) 337–403. [Google Scholar]
  6. J.M. Ball, Some open problems in elasticity, in Geometry, mechanics, and dynamics, P. Newton, P. Holmes and A. Weinstein Eds., Springer, New York (2002) 3–59. [Google Scholar]
  7. D. Balzani, P. Neff, J. Schröder and G.A. Holzapfel, A polyconvex framework for soft biological tissues. Adjustment to experimental data. Int. J. Solids Struct. 43 (2006) 6052–6070. [Google Scholar]
  8. P.E. Bjørstad and O.B. Widlund, Iterative methods for the solution of elliptic problems on regions partitioned into substructures. SIAM J. Numer. Anal. 23 (1986) 1093–1120. [Google Scholar]
  9. D. Brands, A. Klawonn, O. Rheinbach and J. Schröder, Modelling and convergence in arterial wall simulations using a parallel FETI solution strategy. Comput. Methods Biomech. Biomed. Eng. 11 (2008) 569–583. [CrossRef] [Google Scholar]
  10. M. Dryja, A method of domain decomposition for three-dimensional finite element elliptic problem, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations (Paris, 1987), SIAM, Philadelphia (1988) 43–61. [Google Scholar]
  11. M. Dryja, B.F. Smith and O.B. Widlund, Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. SIAM J. Numer. Anal. 31 (1994) 1662–1694. [CrossRef] [MathSciNet] [Google Scholar]
  12. C. Farhat and J. Mandel, The two-level FETI method for static and dynamic plate problems – part I: An optimal iterative solver for biharmonic systems. Comput. Methods Appl. Mech. Eng. 155 (1998) 129–152. [CrossRef] [Google Scholar]
  13. C. Farhat and F.-X. Roux, A method of Finite Element Tearing and Interconnecting and its parallel solution algorithm. Int. J. Numer. Meth. Eng. 32 (1991) 1205–1227. [Google Scholar]
  14. C. Farhat and F.-X. Roux, Implicit parallel processing in structural mechanics, in Computational Mechanics Advances 2, J. Tinsley Oden Ed., North-Holland (1994) 1–124. [Google Scholar]
  15. C. Farhat, J. Mandel and F.X. Roux, Optimal convergence properties of the FETI domain decomposition method. Comput. Methods Appl. Mech. Eng. 115 (1994) 367–388. [Google Scholar]
  16. C. Farhat, M. Lesoinne and K. Pierson, A scalable dual-primal domain decomposition method. Numer. Lin. Alg. Appl. 7 (2000) 687–714. [CrossRef] [Google Scholar]
  17. C. Farhat, K.H. Pierson and M. Lesoinne, The second generation of FETI methods and their application to the parallel solution of large-scale linear and geometrically nonlinear structural analysis problems. Comput. Meth. Appl. Mech. Eng. 184 (2000) 333–374. [CrossRef] [Google Scholar]
  18. C. Farhat, M. Lesoinne, P. Le Tallec, K. Pierson and D. Rixen, FETI-DP: A dual-primal unified FETI method – part I: A faster alternative to the two-level FETI method. Int. J. Numer. Meth. Eng. 50 (2001) 1523–1544. [Google Scholar]
  19. P. Gosselet and C. Rey, Non-overlapping domain decomposition methods in structural mechanics. Arch. Comput. Methods Eng. 13 (2006) 515–572. [CrossRef] [Google Scholar]
  20. G.A. Holzapfel, Nonlinear Solid Mechanics. A continuum approach for engineering. Wiley (2000). [Google Scholar]
  21. A. Klawonn and O. Rheinbach, A parallel implementation of Dual-Primal FETI methods for three dimensional linear elasticity using a transformation of basis. SIAM J. Sci. Comput. 28 (2006) 1886–1906. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Klawonn and O. Rheinbach, Inexact FETI-DP methods. Int. J. Numer. Methods Eng. 69 (2007) 284–307. [CrossRef] [Google Scholar]
  23. A. Klawonn and O. Rheinbach, Robust FETI-DP methods for heterogeneous three dimensional elasticity problems. Comput. Methods Appl. Mech. Eng. 196 (2007) 1400–1414. [CrossRef] [Google Scholar]
  24. A. Klawonn and O. Rheinbach, Highly scalable parallel domain decomposition methods with an application to biomechanics. Z. Angew. Math. Mech. (ZAMM) 90 (2010) 5–32. [CrossRef] [Google Scholar]
  25. A. Klawonn and O.B. Widlund, FETI and Neumann-Neumann iterative substructuring methods: connections and new results. Commun. Pure Appl. Math. 54 (2001) 57–90. [CrossRef] [Google Scholar]
  26. A. Klawonn and O.B. Widlund, Dual-Primal FETI Methods for Linear Elasticity. Commun. Pure Appl. Math. LIX (2006) 1523–1572. [Google Scholar]
  27. A. Klawonn, O.B. Widlund and M. Dryja, Dual-Primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J. Numer. Anal. 40 (2002) 159–179. [CrossRef] [MathSciNet] [Google Scholar]
  28. A. Klawonn, O. Rheinbach and O.B. Widlund, Some computational results for dual-primal FETI methods for elliptic problems in 3D, in Proceedings of the 15th international domain decomposition conference, R. Kornhuber, R.H.W. Hoppe, J. Périaux, O. Pironneau, O.B. Widlund and J. Xu Eds., Springer LNCSE, Lect. Notes Comput. Sci. Eng., Berlin (2005) 361–368. [Google Scholar]
  29. A. Klawonn, L.F. Pavarino and O. Rheinbach, Spectral element FETI-DP and BDDC preconditioners with multi-element subdomains. Comput. Meth. Appl. Mech. Eng. 198 (2008) 511–523. [CrossRef] [Google Scholar]
  30. A. Klawonn, O. Rheinbach and O.B. Widlund, An analysis of a FETI–DP algorithm on irregular subdomains in the plane. SIAM J. Numer. Anal. 46 (2008) 2484–2504. [CrossRef] [MathSciNet] [Google Scholar]
  31. A. Klawonn, P. Neff, O. Rheinbach and S. Vanis, Notes on FETI-DP domain decomposition methods for P-elasticity. Technical report, Universität Duisburg-Essen, Fakultät für Mathematik, http://www.numerik.uni-due.de/publications.shtml (2010). [Google Scholar]
  32. A. Klawonn, P. Neff, O. Rheinbach and S. Vanis, Solving geometrically exact micromorphic elasticity with a staggered algorithm. GAMM Mitteilungen 33 (2010) 57–72. [CrossRef] [Google Scholar]
  33. U. Langer, G. Of, O. Steinbach and W. Zulehner, Inexact data-sparse boundary element tearing and interconnecting methods. SIAM J. Sci. Comput. 29 (2007) 290–314. [CrossRef] [MathSciNet] [Google Scholar]
  34. P. Le Tallec, Numerical methods for non-linear three-dimensional elasticity, in Handbook of numerical analysis 3, J.L. Lions and P. Ciarlet Eds., Elsevier (1994) 465–622. [Google Scholar]
  35. J. Li and O.B. Widlund, FETI-DP, BDDC and Block Cholesky Methods. Int. J. Numer. Methods Eng. 66 (2006) 250–271. [CrossRef] [Google Scholar]
  36. J. Mandel and R. Tezaur, Convergence of a Substructuring Method with Lagrange Multipliers. Numer. Math. 73 (1996) 473–487. [CrossRef] [MathSciNet] [Google Scholar]
  37. J. Mandel and R. Tezaur, On the convergence of a dual-primal substructuring method. Numer. Math. 88 (2001) 543–558. [CrossRef] [MathSciNet] [Google Scholar]
  38. P. Neff, On Korn's first inequality with nonconstant coefficients. Proc. Roy. Soc. Edinb. A 132 (2002) 221–243. [CrossRef] [Google Scholar]
  39. P. Neff, Finite multiplicative plasticity for small elastic strains with linear balance equations and grain boundary relaxation. Contin. Mech. Thermodyn. 15 (2003) 161–195. [CrossRef] [MathSciNet] [Google Scholar]
  40. P. Neff, A geometrically exact viscoplastic membrane-shell with viscoelastic transverse shear resistance avoiding degeneracy in the thin-shell limit. Part I: The viscoelastic membrane-plate. Z. Angew. Math. Phys. (ZAMP) 56 (2005) 148–182. [CrossRef] [Google Scholar]
  41. P. Neff, Local existence and uniqueness for a geometrically exact membrane-plate with viscoelastic transverse shear resistance. Math. Meth. Appl. Sci. (MMAS) 28 (2005) 1031–1060. [CrossRef] [Google Scholar]
  42. P. Neff, Local existence and uniqueness for quasistatic finite plasticity with grain boundary relaxation. Quart. Appl. Math. 63 (2005) 88–116. [MathSciNet] [Google Scholar]
  43. P. Neff, Existence of minimizers for a finite-strain micromorphic elastic solid. Proc. Roy. Soc. Edinb. A 136 (2006) 997–1012. [CrossRef] [Google Scholar]
  44. P. Neff, A finite-strain elastic-plastic Cosserat theory for polycrystals with grain rotations. Int. J. Eng. Sci. 44 (2006) 574–594. [CrossRef] [Google Scholar]
  45. P. Neff and S. Forest, A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling, existence of minimizers, identification of moduli and computational results. J. Elasticity 87 (2007) 239–276. [CrossRef] [MathSciNet] [Google Scholar]
  46. P. Neff and I. Münch, Simple shear in nonlinear Cosserat elasticity: bifurcation and induced microstructure. Contin. Mech. Thermodyn. 21 (2009) 195–221. [CrossRef] [MathSciNet] [Google Scholar]
  47. W. Pompe, Korn's first inequality with variable coefficients and its generalizations. Comment. Math. Univ. Carolinae 44 (2003) 57–70. [Google Scholar]
  48. A. Quarteroni and A. Valli, Numerical Approxiamtion of Partial Differential Equations, in Computational Mathematics 23, Springer Series, Springer, Berlin (1991). [Google Scholar]
  49. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations. Oxford Science Publications, Oxford (1999). [Google Scholar]
  50. J. Schröder and P. Neff, Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions. Int. J. Solids Struct. 40 (2003) 401–445. [Google Scholar]
  51. J. Schröder, P. Neff and D. Balzani, A variational approach for materially stable anisotropic hyperelasticity. Int. J. Solids Struct. 42 (2005) 4352–4371. [Google Scholar]
  52. J. Schröder, P. Neff and V. Ebbing, Anisotropic polyconvex energies on the basis of crystallographic motivated structural tensors. J. Mech. Phys. Solids 56 (2008) 3486–3506. [CrossRef] [MathSciNet] [Google Scholar]
  53. B.F. Smith, P.E. Bjørstad and W. Gropp, Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, Cambridge (1996). [Google Scholar]
  54. E.N. Spadaro, Non-uniqueness of minimizers for strictly polyconvex functionals. Arch. Rat. Mech. Anal. 193 (2009) 659–678. [CrossRef] [Google Scholar]
  55. A. Toselli and O. Widlund, Domain Decomposition Methods – Algorithms and Theory, Springer Series in Computational Mathematics 34. Springer (2004). [Google Scholar]
  56. T. Valent, Boundary Value Problems of Finite Elasticity. Springer, Berlin (1988). [Google Scholar]
  57. K. Weinberg and P. Neff, A geometrically exact thin membrane model-investigation of large deformations and wrinkling. Int. J. Num. Meth. Eng. 74 (2007) 871–893. [CrossRef] [Google Scholar]
  58. O.B. Widlund, An extension theorem for finite element spaces with three applications, in Proceedings of the Second GAMM-Seminar, Kiel January 1986, Notes on Numerical Fluid Mechanics 16, Friedr. Vieweg und Sohn, Braunschweig/Wiesbaden (1987) 110–122. [Google Scholar]

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