Computational Mechanics

, Volume 28, Issue 5, pp 339–350

Solving thermal and phase change problems with the eXtended finite element method

  • R. Merle
  • J. Dolbow

DOI: 10.1007/s00466-002-0298-y

Cite this article as:
Merle, R. & Dolbow, J. Computational Mechanics (2002) 28: 339. doi:10.1007/s00466-002-0298-y


 The application of the eXtended finite element method (X-FEM) to thermal problems with moving heat sources and phase boundaries is presented. Of particular interest is the ability of the method to capture the highly localized, transient solution in the vicinity of a heat source or material interface. This is effected through the use of a time-dependent basis formed from the union of traditional shape functions with a set of evolving enrichment functions. The enrichment is constructed through the partition of unity framework, so that the system of equations remains sparse and the resulting approximation is conforming. In this manner, local solutions and arbitrary discontinuities that cannot be represented by the standard shape functions are captured with the enrichment functions. A standard time-projection algorithm is employed to account for the time-dependence of the enrichment, and an iterative strategy is adopted to satisfy local interface conditions. The separation of the approximation into classical shape functions that remain fixed in time and the evolving enrichment leads to a very efficient solution strategy. The robustness and utility of the method is demonstrated with several benchmark problems involving moving heat sources and phase transformations.

Keywords Partition-of-unity, Phase transformation, Finite element, X-FEM 

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • R. Merle
    • 1
  • J. Dolbow
    • 2
  1. 1.Department of Mechanical Engineering, Ecole Normale Superieure de Cachan, FranceFR
  2. 2.Department of Civil and Environmental Engineering, Duke University, Box 902 87 Durham, North Carolina 27708-0287 e-mail: jdolbow@duke.eduUS

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