Abonnement à la biblothèque: Guest
International Journal for Multiscale Computational Engineering

Publication de 6  numéros par an

ISSN Imprimer: 1543-1649

ISSN En ligne: 1940-4352

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.4 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.3 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 2.2 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.00034 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.46 SJR: 0.333 SNIP: 0.606 CiteScore™:: 3.1 H-Index: 31

Indexed in

AN ADAPTIVE DOMAIN DECOMPOSITION PRECONDITIONER FOR CRACK PROPAGATION PROBLEMS MODELED BY XFEM

Volume 11, Numéro 6, 2013, pp. 633-654
DOI: 10.1615/IntJMultCompEng.2013006012
Get accessGet access

RÉSUMÉ

Application of an algebraic multigrid (AMG) solver to linear systems arising from fracture problems modeled by extended finite elements (XFEM) will often result in poor convergence. This is due to coarsening operators in AMG that disregard the discontinuous enrichment functions and automatically coarsen across cracks. To overcome the AMG coarsening limitation, we propose a multiplicative-Schwarz domain decomposition preconditioner to the generalized minimum residual method. In this approach the domain is decomposed into one uncracked subdomain and multiple cracked subdomains. A cracked subdomain is the domain containing the crack and its enrichment functions and the uncracked subdomain contains the rest of the domain with a one-element-layer overlap between the two. Within the preconditioning scheme, one AMG V-cycle is applied to the uncracked subdomain to obtain an approximate solution while the cracked subdomains (often much smaller compared to the uncracked part) are solved concurrently by a direct solver, thus resolving the error from the discontinuous fields exactly. Hence any black box AMG solver can be used for XFEM, and the need for development of special coarsening procedures that handle enriched degrees of freedom can be avoided. We consider multiple propagating cracks and develop an algorithm that adaptively updates the subdomains, following the cracks. This adaptive scheme can be obtained directly from level set values which are updated with crack growth or from close neighbor search algorithms. The level set update scheme is fast but does not guarantee tight subdomains, while a neighbor search is slower but gives optimal subdomains. The preconditioner is tested on structured and unstructured meshes with multiple propagating cracks and shows convergence rates that are significantly better than a brute force application of AMG to the entire domain.

RÉFÉRENCES
  1. Achtert, E., Böhm, C., Kröger, P., Kunath, P., Pryakhin, A., and Renz, M., Efficient reverse k-nearest neighbor search in arbitrary metric spaces. DOI: 10.1145/1142473.1142531

  2. Anderson, T., Fracture Mechanics: Fundamentals and Applications.

  3. Banks-Sills, L. and Sherman, D., Comparison of methods for calculating stress intensity factors with quarter-point elements. DOI: 10.1007/BF00019788

  4. Belytschko, T. and Black, T., Elastic crack growth in finite elements with minimal remeshing. DOI: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S

  5. Berchtold, S., Ertl, B., Keim, D. A., Kriegel, H. P., and Seidl, T., Fast nearest neighbor search in high-dimensional space. DOI: 10.1109/ICDE.1998.655779

  6. Berger-Vergiat, L., Waisman, H., Hiriyur, B., Tuminaro, R., and Keyes, D., Inexact Schwarz-algebraic multigrid preconditioners for crack problems modeled by extended finite element methods. DOI: 10.1002/nme.3318

  7. Brandt, A., Multi-level adaptive solutions to boundary-value problems. DOI: 10.1090/S0025-5718-1977-0431719-X

  8. Briggs, W. L., Henson, V. E., and McCormick, S. F., A Multigrid Tutorial.

  9. Broberg, K., Crack-growth criteria and non-linear fracture mechanics. DOI: 10.1016/0022-5096(71)90008-1

  10. Bui, H. D., Charras, T., and Cheissoux, J., M&#233;canique de la Rupture: M&#233;thodes Num&#233;riques Pour L&#8216;ing&#233;nieur.

  11. Chan, S., Tuba, I., and Wilson, W., On the finite element method in linear fracture mechanics. DOI: 10.1016/0013-7944(70)90026-3

  12. Decker, R., Source Book on Maraging Steels.

  13. Duarte, C. A., Babu&#353;ka, I., and Oden, J. T., Generalized finite element methods for three-dimensional structural mechanics problems. DOI: 10.1016/S0045-7949(99)00211-4

  14. Erdogan, F. and Sih, G. C., On the crack extension in plate under plane loading and transverse shear. DOI: 10.1115/1.3656897

  15. Fan, R. and Fish, J., The <i>rs</i>-method for material failure simulations. DOI: 10.1002/nme.2134

  16. Farhat, C., Mandel, J., and Roux, F. X., Optimal convergence properties of the FETI domain decomposition method. DOI: 10.1016/0045-7825(94)90068-X

  17. Farhat, C. and Roux, F. X., A method of finite element tearing and interconnecting and its parallel solution algorithm. DOI: 10.1002/nme.1620320604

  18. Fish, J., The <i>s</i>-version of the finite element method. DOI: 10.1016/0045-7949(92)90287-A

  19. Fish, J. and Markolefas, S., Adaptive <i>s</i>-method for linear elastostatics. DOI: 10.1016/0045-7825(93)90032-S

  20. Gee, M.W., Hu, J. J., and Tuminaro, R. S., A new smoothed aggregation multigrid method for anisotropic problems. DOI: 10.1002/nla.593

  21. Goodman, J. E. and O&#8216;Rourke, J., Handbook of Discrete and Computational Geometry. DOI: 10.1201/9781420035315

  22. Gosz, M., Dolbow, J., and Moran, B., Domain integral formulation for stress intensity factor computation along curved threedimensional interface cracks. DOI: 10.1016/S0020-7683(97)00132-7

  23. Gosz, M. and Moran, B., An interaction energy integral method for computation of mixed-mode stress intensity factors along non-planar crack fronts in three dimensions. DOI: 10.1016/S0013-7944(01)00080-7

  24. Gravouil, A., Rannou, J., and Ba&#239;etto, M.-C., A local multi-grid X-FEM approach for 3D fatigue crack growth. DOI: 10.1007/s12289-008-0212-z

  25. Heroux, M. A., Bartlett, R. A., Howle, V. E., Hoekstra, R. J., Hu, J., Kolda, T. G., Lehoucq, R. B., Long, K. R., Pawlowski, R. P., Phipps, E. T., Salinger, A. G., Thornquist, H. K., Tuminaro, R. S., Willenbring, J. M., Williams, A., and Stanley, K. S., An overview of the Trilinos project. DOI: 10.1145/1089014.1089021

  26. Hiriyur, B., Tuminaro, R., Waisman, H., Boman, E., and Keyes, D., A quasi-algebraic multigrid approach to fracture problems based on the extended finite element method. DOI: 10.1137/110819913

  27. Hughes, T. J. R., The Finite Element Method: Linear Static And Dynamic Finite Element Analysis.

  28. Kishimoto, K., Aoki, S., and Sakata, M., On the path independent integral-&#309;. DOI: 10.1016/0013-7944(80)90015-6

  29. Krauthgamer, R. and Lee, J., The black-box complexity of nearest-neighbor search. DOI: 10.1016/j.tcs.2005.09.017

  30. Li, F. Z., Shih, C. F., and Needleman, A., A comparison of methods for calculating energy release rates. DOI: 10.1016/0013-7944(85)90029-3

  31. Liu, X. Y., Xiao, Q. Z., and Karihaloo, B. L., XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials. DOI: 10.1002/nme.906

  32. Menk, A. and Bordas, S. P. A., A robust preconditioning technique for the extended finite element method. DOI: 10.1002/nme.3032

  33. Mo&#235;s, N., Dolbow, J., and Belytschko, T., A finite element method for crack growth without remeshing. DOI: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J

  34. Mo&#235;s, N., Gravouil, A., and Belytschko, T., Non-planar 3D crack growth by the extended finite element and level sets&mdash;Part I: Mechanical model. DOI: 10.1002/nme.429

  35. Munjiza, A. A., The Combined Finite-Discrete Element Method. DOI: 10.1002/0470020180

  36. Nagashima, T., Omoto, Y., and Tani, S., Stress intensity factor analysis of interface cracks using X-FEM. DOI: 10.1002/nme.604

  37. Nuismer, R. J., An energy release rate criterion for mixed mode fracture. DOI: 10.1007/BF00038891

  38. Olson, L. N., Schroder, J. B., and Tuminaro, R. S., A general interpolation strategy for algebraic multigrid using energy minimization. DOI: 10.1137/100803031

  39. Oosterlee, C.W. and Washio, T., On the use of multigrid as a preconditioner.

  40. Osher, S. and Sethian, J. A., Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. DOI: 10.1016/0021-9991(88)90002-2

  41. Parks, D. M., A stiffness derivative finite element technique for determination of crack tip stress intensity factors. DOI: 10.1007/BF00155252

  42. Parsons, I. D. and Hall, J. F., The multigrid method in solid mechanics: Part I&mdash;algorithm description and behaviour. DOI: 10.1002/nme.1620290404

  43. Parsons, I. D. and Hall, J. F., The multigrid method in solid mechanics: Part II&mdash;practical applications. DOI: 10.1002/nme.1620290405

  44. Passieux, J. C., Gravouil, A., Rh&#233;thor&#233;, J., and Baietto, M. C., Direct estimation of generalised stress intensity factors using threescale concurrent multigrid X-FEM. DOI: 10.1002/nme.3037

  45. Pommier, S., Gravouil, A., Mo&#235;s, N., and Combescure, A., Extended Finite Element Method for Crack Propagation. DOI: 10.1002/9781118622650

  46. Rannou, J., Gravouil, A., and Baietto-Dubourg, M. C., A local multigrid X-FEM strategy for 3-D crack propagation. DOI: 10.1002/nme.2427

  47. Rice, J. R., A path independent integral and the approximate analysis of strain concentration by notches and cracks. DOI: 10.1115/1.3601206

  48. Rybicki, E. and Kanninen, M., A finite element calculation of stress intensity factors by a modified crack closure integral. DOI: 10.1016/0013-7944(77)90013-3

  49. Saad, Y. and Schultz, M. H., GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. DOI: 10.1137/0907058

  50. Sethian, J. A., Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science.

  51. Shih, C. F., Lorenzi, H. G., and German, M. D., Crack extension modeling with singular quadratic isoparametric elements. DOI: 10.1007/BF00034654

  52. Sih, G. C., Strain-energy-density factor applied to mixed mode crack problems. DOI: 10.1007/BF00035493

  53. Smith, B. F., Bjorstad, P., and Gropp, W., Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations.

  54. Sukumar, N., Chopp, D. L., Mo&#235;s, N., and Belytschko, T., Modeling holes and inclusions by level sets in the extended finite element method. DOI: 10.1016/S0045-7825(01)00215-8

  55. Toselli, A. and Widlund, O., Domain Decomposition Methods &#8211; Algorithms and Theory. DOI: 10.1007/b137868

  56. Tuminaro, R. S., Parallel smoothed aggregation multigrid: aggregation strategies on massively parallel machines.

  57. Tuminaro, R. S. and Tong, C., Parallel smoothed aggregation multigrid: Aggregation strategies on massively parallel machines. DOI: 10.1109/SC.2000.10008

  58. Van&#283;k, P., Mandel, J., and Brezina, M., Algebraic multigrid by smoothed aggregation for second and fourth order elliptic problems. DOI: 10.1007/BF02238511

  59. Waisman, H., An analytical stiffness derivative extended finite element technique for extraction of crack tip strain energy release rates. DOI: 10.1016/j.engfracmech.2010.08.015

  60. Waisman, H., Fish, J., Tuminaro, R. S., and Shadid, J., The Generalized Global Basis (GGB) method. DOI: 10.1002/nme.1107

  61. Waisman, H., Fish, J., Tuminaro, R. S., and Shadid, J., Acceleration of the Generalized Global Basis (GGB) method for nonlinear problems. DOI: 10.1016/j.jcp.2005.04.016

  62. Williams, J. G. and Ewing, P. D., Fracture under complex stress, the angled crack problem. DOI: 10.1007/BF00962967

  63. Williams, M. L., On the stress distribution at the base of a stationary crack.

  64. Wyart, E., Duflot, M., Coulon, D., Martiny, P., Pardoen, T., and Remacle, J.-F., A substructured FE-shell/XFE-3D method for crack analysis in thin-walled structures. DOI: 10.1002/nme.2029

  65. Wyart, E., Duflot, M., Coulon, D., Martiny, P., Pardoen, T., Remacle, J.-F., and Lani, F., Substructuring FE-XFE approaches applied to three-dimensional crack propagation. DOI: 10.1016/j.cam.2006.03.066

  66. Xu, J. and Zikatanov, L. T., On Multigrid Methods for Generalized Finite Element Methods. DOI: 10.1007/978-3-642-56103-0_28

  67. Zamani, A., Gracie, R., and Eslami, R., Cohesive and non-cohesive fracture by higher-order enrichment of xfem. DOI: 10.1002/nme.3329

CITÉ PAR
  1. Lan Mengyu, Waisman Haim, Harari Isaac, A High-order extended finite element method for extraction of mixed-mode strain energy release rates in arbitrary crack settings based on Irwin's integral, International Journal for Numerical Methods in Engineering, 96, 12, 2013. Crossref

  2. Casoni E., Jérusalem A., Samaniego C., Eguzkitza B., Lafortune P., Tjahjanto D. D., Sáez X., Houzeaux G., Vázquez M., Alya: Computational Solid Mechanics for Supercomputers, Archives of Computational Methods in Engineering, 22, 4, 2015. Crossref

  3. Gupta V., Duarte C.A., Babuška I., Banerjee U., Stable GFEM (SGFEM): Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 289, 2015. Crossref

  4. Mobasher Mostafa E., Waisman Haim, Adaptive modeling of damage growth using a coupled FEM/BEM approach, International Journal for Numerical Methods in Engineering, 105, 8, 2016. Crossref

  5. Ventura Giulio, Tesei Claudia, Stabilized X-FEM for Heaviside and Nonlinear Enrichments, in Advances in Discretization Methods, 12, 2016. Crossref

  6. Berger-Vergiat Luc, Waisman Haim, An overlapping Domain Decomposition preconditioning method for monolithic solution of shear bands, Computer Methods in Applied Mechanics and Engineering, 318, 2017. Crossref

  7. Brenner Susanne C., Davis Christopher B., Sung Li-yeng, A Two-Level Additive Schwarz Domain Decomposition Preconditioner for a Flat-Top Partition of Unity Method, in Meshfree Methods for Partial Differential Equations VIII, 115, 2017. Crossref

  8. Babuška Ivo, Banerjee Uday, Kergrene Kenan, Strongly stable generalized finite element method: Application to interface problems, Computer Methods in Applied Mechanics and Engineering, 327, 2017. Crossref

  9. Nguyen Nhu, Yvonnet J., Réthoré J., Tran A. B., Identification of fracture models based on phase field for crack propagation in heterogeneous lattices in a context of non-separated scales, Computational Mechanics, 63, 5, 2019. Crossref

  10. Agathos Konstantinos, Bordas Stéphane P.A., Chatzi Eleni, Improving the conditioning of XFEM/GFEM for fracture mechanics problems through enrichment quasi-orthogonalization, Computer Methods in Applied Mechanics and Engineering, 346, 2019. Crossref

  11. Xing Chen, Zhou Chuwei, Finite element modeling of crack growth in thin-wall structures by method of combining sub-partition and substructure, Engineering Fracture Mechanics, 195, 2018. Crossref

  12. Hun Darith‐Anthony, Guilleminot Johann, Yvonnet Julien, Bornert Michel, Stochastic multiscale modeling of crack propagation in random heterogeneous media, International Journal for Numerical Methods in Engineering, 119, 13, 2019. Crossref

  13. Jomo J.N., de Prenter F., Elhaddad M., D'Angella D., Verhoosel C.V., Kollmannsberger S., Kirschke J.S., Nübel V., van Brummelen E.H., Rank E., Robust and parallel scalable iterative solutions for large-scale finite cell analyses, Finite Elements in Analysis and Design, 163, 2019. Crossref

  14. Fillmore Travis B., Gupta Varun, Duarte Carlos Armando, Preconditioned Conjugate Gradient Solvers for the Generalized Finite Element Method, in Meshfree Methods for Partial Differential Equations IX, 129, 2019. Crossref

  15. de Prenter F., Verhoosel C.V., van Brummelen E.H., Preconditioning immersed isogeometric finite element methods with application to flow problems, Computer Methods in Applied Mechanics and Engineering, 348, 2019. Crossref

  16. Rao S.S. Durga, Raju Sethuraman, Orthogonalized Generalized Iso-Geometric Analysis (OGIGA) and its applications to problems of fracture mechanics, Computer Methods in Applied Mechanics and Engineering, 372, 2020. Crossref

  17. de Assis Felipe Mouallem, Gomes Guilherme Ferreira, Crack identification in laminated composites based on modal responses using metaheuristics, artificial neural networks and response surface method: a comparative study, Archive of Applied Mechanics, 91, 10, 2021. Crossref

  18. Svolos Lampros, Berger-Vergiat Luc, Waisman Haim, Updating strategy of a domain decomposition preconditioner for parallel solution of dynamic fracture problems, Journal of Computational Physics, 422, 2020. Crossref

  19. Neiva Eric, Badia Santiago, Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems, Computer Methods in Applied Mechanics and Engineering, 380, 2021. Crossref

  20. Badia Santiago, Neiva Eric, Verdugo Francesc, Linking ghost penalty and aggregated unfitted methods, Computer Methods in Applied Mechanics and Engineering, 388, 2022. Crossref

  21. Chen Xingding, Cai Xiao-Chuan, A recycling preconditioning method with auxiliary tip subspace for elastic crack propagation simulation using XFEM, Journal of Computational Physics, 452, 2022. Crossref

  22. Tian Wei, Huang Jingjing, Jiang Yi, Chen Rongliang, A parallel scalable domain decomposition preconditioner for elastic crack simulation using XFEM, International Journal for Numerical Methods in Engineering, 123, 15, 2022. Crossref

  23. Agathos Konstantinos, Dodwell Tim, Chatzi Eleni, Bordas Stéphane P.A., An adapted deflated conjugate gradient solver for robust extended/generalised finite element solutions of large scale, 3D crack propagation problems, Computer Methods in Applied Mechanics and Engineering, 395, 2022. Crossref

  24. Bakalakos Serafeim, Georgioudakis Manolis, Papadrakakis Manolis, Domain decomposition methods for 3D crack propagation problems using XFEM, Computer Methods in Applied Mechanics and Engineering, 2022. Crossref

Portail numérique Bibliothèque numérique eBooks Revues Références et comptes rendus Collections Prix et politiques d'abonnement Begell House Contactez-nous Language English 中文 Русский Português German French Spain