Skip to main content
SpringerLink
Log in

Speeding-up simulation of cogging process by multigrid method

  • Original Research
  • Published:
International Journal of Material Forming Aims and scope Submit manuscript

Abstract

Calculation time of some material forming processes is tremendously expensive which makes reducing computational time one of the most urgent challenges in this domain. Among strategies that have been developed to speed-up calculations, one of the most flexible solutions is to utilize enhanced linear solvers such as Multi-Grid algorithm. It consists in using several levels of meshes of the same domain in order to more efficiently solve the systems of equations derived from the discretized problem. The speed-up results from the efficiency of coarse meshes in computing the low frequencies of the residual while fine meshes are more efficient in reducing the high frequencies of the residual. The method is integrated in the commercial software Forge® and applied to the industrial cogging process. The obtained results show that the speed-up depends on the number of nodes; for an industrial scale mesh of 50,000 nodes, the multigrid technique allows dividing the computational time by a factor of two.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Dedieu C, Barasinski A, Chinesta F et al (2016) About the origins of residual stresses in in situ consolidated thermoplastic composite rings. Int J Mater Form. https://doi.org/10.1007/s12289-016-1319-2

    Google Scholar 

  2. Dedieu C, Barasinski A, Chinesta F et al (2016) On the prediction of residual stresses in automated tape placement. Int J Mater Form. https://doi.org/10.1007/s12289-016-1307-6

  3. Lopez E, Abisset-Chavanne E, Lebel F et al (2016) Flow modeling of linear and nonlinear fluids in two and three scale fibrous fabrics. Int J Mater Form 9:215. https://doi.org/10.1007/s12289-015-1224-0

    Article  Google Scholar 

  4. Ammar A, Abisset-Chavanne E, Chinesta F et al (2016) Flow modelling of quasi-Newtonian fluids in two-scale fibrous fabrics. Int J Mater Form. https://doi.org/10.1007/s12289-016-1300-0

  5. Leon A, Barasinski A, Chinesta F (2017) Microstructural analysis of pre-impreganted tapes consolidation. Int J Mater Form 10:369. https://doi.org/10.1007/s12289-016-1285-8

    Article  Google Scholar 

  6. Lopez E, Abisset-Chavanne E, Lebel F et al (2016) Advanced thermal simulation of processes involving materials exhibiting fine-scale microstructures. Int J Mater Form 9:179. https://doi.org/10.1007/s12289-015-1222-2

    Article  Google Scholar 

  7. Cueto E, Chinesta F (2015) Meshless methods for the simulation of material forming. Int J Mater Form 8:25. https://doi.org/10.1007/s12289-013-1142-y

    Article  Google Scholar 

  8. Khaled M, Ramadan M, Fourment L (2016) Thermal modeling of cogging process using finite element method. AIP Conf Proc 1769:060008

    Article  Google Scholar 

  9. Ramadan M, Khaled M, Fourment L (2016) Application of multi-grid method on the simulation of incremental forging processes. AIP Conf Proc 1769:130004

    Article  Google Scholar 

  10. Ramadan M, Fourment L, Perchat E (2008) A multi-levels method with two meshes for speeding-up incremental processes such as cogging. In: 9th international conference on technology of plasticity, ICTP, pp 1747–175

  11. Guo RP, Xu L, Zong BY, Yang R (2016) Preparation and ring rolling processing of large size Ti-6Al-4V powder compact. Mater Des 99:341–348. https://doi.org/10.1016/j.matdes.2016.02.128

    Article  Google Scholar 

  12. Wang C, Geijselaers HJM, Omerspahic E, Recina V, van den Boogaard AH (2016) Influence of ring growth rate on damage development in hot ring rolling. J Mater Process Technol 227:268–280. https://doi.org/10.1016/j.jmatprotec.2015.08.017

    Article  Google Scholar 

  13. Ramadan M, Fourment L, Digonnet H (2014) Fast resolution of incremental forming processes by the multi-mesh method. Application to cogging. Int J Mater Form 7(2):207–219. https://doi.org/10.1007/s12289-012-1121-8

    Article  Google Scholar 

  14. Ramadan M, Fourment L, Digonnet H (2009) A parallel two mesh method for speeding-up processes with localized deformations: application to cogging. Int J Mater Form 2(1):581–584. https://doi.org/10.1007/s12289-009-0440-x

    Article  Google Scholar 

  15. Khaled M, Ramadan M, Elmarakbi A, Fourment L (2015) Simulation of incremental forming processes using a thermo-mechanical partitioned algorithm. Key Eng Mater 651-653:1331–1336. https://doi.org/10.4028/www.scientific.net/KEM.651-653.1331

    Article  Google Scholar 

  16. Wasserman M, Mor-Yossef Y, Greenberg JB (2016) A positivity-preserving, implicit defect-correction multigrid method for turbulent combustion. J Comput Phys 316:303–337. https://doi.org/10.1016/j.jcp.2016.04.005

    Article  MathSciNet  MATH  Google Scholar 

  17. Cools S, Vanroose W (2016) A fast and robust computational method for the ionization cross sections of the driven Schrödinger equation using an O(N) multigrid-based scheme. J Comput Phys 308:20–39

    Article  MathSciNet  MATH  Google Scholar 

  18. Bauer P, Klement V, Oberhuber T, Žabka V (2016) Implementation of the Vanka-type multigrid solver for the finite element approximation of the Navier–stokes equations on GPU. Comput Phys Commun 200:50–56. https://doi.org/10.1016/j.cpc.2015.10.021

    Article  MathSciNet  Google Scholar 

  19. Augustin CM, Neic A, Liebmann M, Prassl AJ, Niederer SA, Haase G, Plank G (2016) Anatomically accurate high resolution modeling of human whole heart electromechanics: a strongly scalable algebraic multigrid solver method for nonlinear deformation. J Comput Phys 305:622–646, ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2015.10.045

    Article  MathSciNet  MATH  Google Scholar 

  20. Bhowmik SK (2015) A multigrid preconditioned numerical scheme for a reaction–diffusion system. Appl Math Comput 254:266–276. https://doi.org/10.1016/j.amc.2014.12.062

    MathSciNet  MATH  Google Scholar 

  21. Bolten M, Huckle TK, Kravvaritis CD (2016) Sparse matrix approximations for multigrid methods. Linear Algebra Appl 502:58–76. https://doi.org/10.1016/j.laa.2015.11.008

    Article  MathSciNet  MATH  Google Scholar 

  22. Rauwoens P, Troch P, Vierendeels J (2015) A geometric multigrid solver for the free-surface equation in environmental models featuring irregular coastlines. J Comput Appl Math 289:22–36. https://doi.org/10.1016/j.cam.2015.03.029

    Article  MathSciNet  MATH  Google Scholar 

  23. Jiang Y, Xu X (2015) Multigrid methods for space fractional partial differential equations. J Comput Phys 302:374–392. https://doi.org/10.1016/j.jcp.2015.08.052

    Article  MathSciNet  MATH  Google Scholar 

  24. Kang KS (2015) Scalable implementation of the parallel multigrid method on massively parallel computers. Comput Math Appl 70(11):2701–2708, ISSN 0898-1221. https://doi.org/10.1016/j.camwa.2015.07.023

    Article  MathSciNet  Google Scholar 

  25. Sviercoski RF, Popov P, Margenov S (2015) An analytical coarse grid operator applied to a multiscale multigrid method. J Comput Appl Math 287:207–219. ISSN 0377-0427. https://doi.org/10.1016/j.cam.2015.03.001

    Article  MathSciNet  MATH  Google Scholar 

  26. Santiago CD, Marchi CH, Souza LF (2015) Performance of geometric multigrid method for coupled two-dimensional systems in CFD. Appl Math Model 39(9):2602–2616. https://doi.org/10.1016/j.apm.2014.10.067

    Article  MathSciNet  Google Scholar 

  27. Ma W, Lu Z, Zhang J (2015) GPU parallelization of unstructured/hybrid grid ALE multigrid unsteady solver for moving body problems. Comput Fluids 110:122–135. https://doi.org/10.1016/j.compfluid.2014.11.012

    Article  MathSciNet  MATH  Google Scholar 

  28. Gandham R, Esler K, Zhang Y (2014) A GPU accelerated aggregation algebraic multigrid method. Comp Math Appl 68(10):1151–1160. https://doi.org/10.1016/j.camwa.2014.08.022

    Article  MathSciNet  MATH  Google Scholar 

  29. Rey B, Mocellin K, Fourment L (2008) A node-nested Galerkin multigrid method for metal forging simulation. Comput Vis Sci 11(1):17–25. https://doi.org/10.1007/s00791-006-0054-5

    Article  MathSciNet  Google Scholar 

  30. Mocellin K, Fourment L, Coupez T, Chenot J-L (2001) Toward large scale FE computation of hot forging process using iterative solvers, parallel computation and multigrid algorithms. Int J Numer Methods Eng 52(5–6):473–488. https://doi.org/10.1002/nme.304

    Article  MATH  Google Scholar 

  31. Feng YT, Peric D, Owen DRJ (1997) A non-nested Galerkin multi-grid method for solving linear and nonlinear solid mechanics problems. Comput Methods Appl Mech Eng 144(3-4):307–325. https://doi.org/10.1016/S0045-7825(96)01183-8

    Article  MathSciNet  MATH  Google Scholar 

  32. Arnold DN, Brezzi F, Fortin M (1984) A stable finite element for the stokes equations. Calcolo 21(4):337–344. https://doi.org/10.1007/BF02576171

    Article  MathSciNet  MATH  Google Scholar 

  33. Coupez T (1991) Grandes déformations et remaillage automatique. Ph.D. Thesis, Mines Paristech, France

  34. Fourment L, Chenot JL, Mocellin K (1999) Numerical formulations and algorithms for solving contact problems in metal forming simulation. Int J Numer Methods Eng 46(9):1435–1462. https://doi.org/10.1002/(SICI)1097-0207(19991130)46:9<1435::AID-NME707>3.0.CO;2-9

    Article  MATH  Google Scholar 

  35. Sameh AH, Kuck DJ (1977) Parallel direct linear system solvers - a survey. Math Comput Simul 19(4):272–277, ISSN 0378-4754. https://doi.org/10.1016/0378-4754(77)90044-1

    Article  MathSciNet  MATH  Google Scholar 

  36. Jain SK, Ray RK, Bhavsar A (2015) Iterative solvers for image denoising with diffusion models: a comparative study. Comput Math Appl 70(3):191–211, ISSN 0898-1221. https://doi.org/10.1016/j.camwa.2015.04.009

    Article  MathSciNet  Google Scholar 

  37. Pearson JW (2016) Fast iterative solvers for large matrix systems arising from time-dependent stokes control problems. Appl Numer Math 108:87–101, ISSN 0168-9274. https://doi.org/10.1016/j.apnum.2016.05.002

    Article  MathSciNet  MATH  Google Scholar 

  38. Benzi M, Golub G, Liesen J (2005) Numerical solution of saddle point problems. Acta Numer 14:1–137. https://doi.org/10.1017/S0962492904000212

    Article  MathSciNet  MATH  Google Scholar 

  39. Borzacchiello D, Leriche E, Blottière B, Guillet J (2017) Box-relaxation based multigrid solvers for the variable viscosity stokes problem. Comput Fluids 156:515–525. https://doi.org/10.1016/j.compfluid.2017.08.027

    Article  MathSciNet  MATH  Google Scholar 

  40. Burstedde C, Ghattas O, Stadler G, Tu T, Wilcox LC (2009) Parallel scalable adjoint-based adaptive solution of variable-viscosity stokes flow problems. Comput Methods Appl Mech Eng 198(21–26):1691–1700, ISSN 0045-7825. https://doi.org/10.1016/j.cma.2008.12.015

    Article  MATH  Google Scholar 

  41. Elman H, Howle VE, Shadid J, Shuttleworth R, Tuminaro R (2006) Block preconditioners based on approximate commutators. SIAM J Sci Comput 27(5):1651–1668. https://doi.org/10.1137/040608817

    Article  MathSciNet  MATH  Google Scholar 

  42. Oosterlee CW, Gaspar FJ (2008) Multigrid relaxation methods for systems of saddle point type. Appl Numer Math 58(12):1933–1950. https://doi.org/10.1016/j.apnum.2007.11.014

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the consortium « club forgeage libre » which gathered the following industries: ArcelorMittal, Cézus (Areva), Sfarsteel (Areva), Aubert & Duval and Manoir industries and the software developer Transvalor.

Author information

Authors and Affiliations

  1. Energy and Thermo-Fluid Group, School of Engineering, International University of Beirut, PO Box 146404, Beirut, Lebanon

    Mohamad Ramadan & Mahmoud Khaled

  2. FCLAB, CNRS, Univ. Bourgogne Franche-Comté, Belfort cedex, France

    Mohamad Ramadan

  3. Univ Paris Diderot, Sorbonne Paris Cité, Paris Interdisciplinary Energy Research Institute (PIERI), Paris, France

    Mahmoud Khaled

  4. MINES ParisTech, PSL Research University, CEMEF, CNRS UMR 7635, CS 10207 rue Claude Daunesse, 06904 Sophia Antipolis Cedex, France

    Lionel Fourment

Authors
  1. Mohamad Ramadan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mahmoud Khaled
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lionel Fourment
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohamad Ramadan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramadan, M., Khaled, M. & Fourment, L. Speeding-up simulation of cogging process by multigrid method. Int J Mater Form 12, 45–55 (2019). https://doi.org/10.1007/s12289-018-1405-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12289-018-1405-8

Keywords

Search

Navigation