An optimally-coupled multi-time stepping method for transient heat conduction simulation for additive manufacturing

Lin Cheng, Gregory J. Wagner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


With growing application of additive manufacturing (AM) in industry, simulation of transient heat conduction during the AM process has drawn increasing attention. However, detailed simulation with acceptable accuracy is extremely time consuming because of the large range of time scales involved in the problem. In this work, a multi-time stepping method using different timesteps in multiple subdomains is developed to accelerate transient heat conduction simulation. A Dirichlet–Robin iterative coupling scheme is proposed to enforce continuity at the interfaces between different subdomains. This allows numerical stability of the multi-timestep​ model, even with disparate materials or meshes on either side of the subdomain interfaces. Specifically, an optimal approximation for the Schur complement matrix is derived using a one-dimensional (1D) model, which avoids the instabilities encountered when using a Dirichlet–Neumann coupling formulation and allows convergence of the iterative coupling scheme in only one iteration at each timestep. Several numerical examples are studied to evaluate the stability, convergence and performance of the method. It is found that the proposed method is robust and stable for all choices of material parameters, unlike the conventional Dirichlet–Neumann coupling scheme. To demonstrate the use of the method for AM, a simulation representative of a single laser track is performed and compared with line heat source model approach. It is found that the proposed method not only accelerates the simulation by a factor of more than 100, but gives very good accuracy for temperature in the melt pool region.

Original languageEnglish (US)
Article number113825
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Aug 1 2021


  • Dirichlet–Robin coupling
  • Metal additive manufacturing
  • Multi-time scale modeling
  • Schur complement matrix
  • Transient heat transfer

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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