International Journal of Material Forming

, Volume 12, Issue 1, pp 45–55 | Cite as

Speeding-up simulation of cogging process by multigrid method

  • Mohamad RamadanEmail author
  • Mahmoud Khaled
  • Lionel Fourment
Original Research


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.


Multigrid Iterative solver Meshing Material forming Cogging Process simulation finite element method 



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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  • Mohamad Ramadan
    • 1
    • 2
    Email author
  • Mahmoud Khaled
    • 1
    • 3
  • Lionel Fourment
    • 4
  1. 1.Energy and Thermo-Fluid Group, School of EngineeringInternational University of BeirutBeirutLebanon
  2. 2.FCLAB, CNRS, Univ. Bourgogne Franche-ComtéBelfort cedexFrance
  3. 3.Univ Paris Diderot, Sorbonne Paris Cité, Paris Interdisciplinary Energy Research Institute (PIERI)ParisFrance
  4. 4.MINES ParisTech, PSL Research University, CEMEF, CNRS UMR 7635, CS 10207 rue Claude Daunesse06904 Sophia Antipolis CedexFrance

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