Application of a recycling Krylov subspace strategy for discrete element method applied to brittle crack problems

References

• Cundall , P. A. and Strack , O. D. L. 1979 . A discrete numerical model for granular assemblies . Géotechnique , 29 : 47 – 65 .
   Web of Science ®Google Scholar
• D’Addetta , G. A. 2004 . Discrete models for cohesive frictional materials , Stuttgart University . PhD thesis
   Google Scholar
• Delaplace , A. 2009 . Tensile damage response from discrete element virtual testing . Geomechanics and Geoengineering , 4 ( 1 ) : 79 – 89 .
   Google Scholar
• Delaplace , A. and Desmorat , R. 2007 . Discrete 3D model as complimentary numerical testing for anisotropic damage . International Journal of Fracture , 148 : 115 – 128 .
   Web of Science ®Google Scholar
• der Sluis , A. V. and der Vorst , H. A. V. 1986 . The rate of convergence of conjugate gradients . Numer. Math. , 48 : 543 – 560 .
   Google Scholar
• Farhat , C. and Roux , F. 1994 . Implicit parallel processing in structural mechanics . Computational Mechanics Advances , 2 : 1 – 124 .
   Google Scholar
• Gosselet , P. and Rey , C. On a selective reuse of Krylov subspaces in Newton-Krylov approaches for nonlinear elasticity . 14th International Conference on Domain Decomposition Methods .
   Google Scholar
• Gosselet , P. and Rey , C. 2006 . Non-overlapping domain decomposition methods in structural mechanics . Arch. Comput. Meth. Engng. , 13 : 515 – 572 .
   Web of Science ®Google Scholar
• Herrmann , H. J. and Roux , S. 1990 . Statistical models for the fracture of disordered media , Amsterdam : Elsevier Science Publishers .
   Google Scholar
• Moukarzel , C. and Herrmann , H. J. 1992 . A vectorizable random lattice . J. Stat. Phys. , 68 : 911 – 923 .
   Web of Science ®Google Scholar
• Nukala , P. and Simunovic , S. 2004 . An efficient block-circulant preconditioner for simulating fracture using large fuse networks . J. Phys. A : Math. Gen. , 37 : 2093 – 2103 .
   Google Scholar
• Nukala , P. and Simunovic , S. Large scale simulation of fracture network . ICF 11 - 11th International Conference on Fracture .
   Google Scholar
• Paige , C. , Parlett , B. N. and der Vorst , H. V. 1995 . Approximate solutions and eigenvalue bounds from Krylov subspaces . Num. Lin. Alg. Appl. , 2 : 115 – 133 .
   Web of Science ®Google Scholar
• Potyondy , D. O. and Cundall , P. A. 2004 . A bonded-particle model for rock . International Journal of Rock Mechanics and Mining Sciences , 41 ( 8 ) : 1329 – 1364 .
   Web of Science ®Google Scholar
• Rey , C. 1996 . An acceleration technique for the solution of non-linear elasticity problems by domain decomposition . C. R. Acad. Sci. , 322 : 601 – 606 .
   Google Scholar
• Rey , C. and Risler , C. 1998 . A Rayleigh-Ritz preconditioner for the iterative solution to large scale nonlinear problem . Numerical Algorithms , 17 : 279 – 311 .
   Google Scholar
• Risler , C. and Rey , C. 2000 . Iterative accelerating algorithms with Krylov subspaces for the solution to large-scale nonlinear problems . Numerical Algorithms , 23 : 1 – 30 .
   Web of Science ®Google Scholar
• Saad , Y. 2000 . Iterative methods for sparse linear systems , 3rd edition , PWS Publishing Company .
   Google Scholar
• Saad , Y. , Yeung , M. , Erhel , J. and Guyomarc’h , F. 2000 . A deflated version of the conjugate gradient algorithm . SIAM J. Sci. Comput. , 21 : 1909 – 1926 .
   Web of Science ®Google Scholar
• Van Mier , J. G. M. , Van Vliet , M. R. A. and Wang , T. K. 2002 . Fracture mechanisms in particle composites : statistical aspects in lattice type analysis . Mech. Mater , 34 : 705 – 724 .
   Web of Science ®Google Scholar
• Yip , M. , Li , Z. , Liao , B.-S. and Bolander , J. 2006 . Irregular lattice models of fracture of multiphase particulate materials . International Journal of Fracture , 140 : 113 – 124 .
   Google Scholar