A multigrid solver for phase field simulation of microstructure evolution

  • Authors:

  • Liesbeth Vanherpe;Frank Wendler;Britta Nestler;Stefan Vandewalle

  • Affiliations:

  • Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium;Department of Computer Science, Karlsruhe University of Applied Sciences, Moltkestraíe 30, 76133 Karlsruhe, Germany;Department of Computer Science, Karlsruhe University of Applied Sciences, Moltkestraíe 30, 76133 Karlsruhe, Germany;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001 Leuven, Belgium

  • Venue:
  • Mathematics and Computers in Simulation
  • Year:
  • 2010

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Abstract

This paper presents a semi-implicit numerical method for the simulation of grain growth in two dimensions with a multi-phase field model. To avoid the strong stability condition of traditional explicit methods, a first-order, semi-implicit discretisation scheme is employed, which offers a good compromise with regard to memory intensity and computational requirements. A nonlinear multigrid solver based on the Full Approximation Scheme is implemented to solve the equations resulting from this discretisation. Simulations with the multigrid solver show that the solver has grid size independent convergence properties and is faster than a standard first-order explicit solver. As such, the multigrid solver promises to be a reliable additional computational tool for the simulation of microstructural evolution. A comparison with existing alternatives remains, however, subject of further investigation. To validate the implementation, the results of specific test cases are studied.