Commun. Comput. Phys., 11 (2012), pp. 1697-1717.

Parareal in Time Simulation of Morphological Transformation in Cubic Alloys with Spatially Dependent Composition

Li-Ping He 1*, Minxin He 1

1 Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China.

Received 11 March 2010; Accepted (in revised version) 9 September 2011
Available online 12 January 2012


In this paper, a reduced morphological transformation model with spatially dependent composition and elastic modulus is considered. The parareal in time algorithm introduced by Lions et al. is developed for longer-time simulation. The fine solver is based on a second-order scheme in reciprocal space, and the coarse solver is based on a multi-model backward Euler scheme, which is fast and less expensive. Numerical simulations concerning the composition with a random noise and a discontinuous curve are performed. Some microstructure characteristics at very low temperature are obtained by a variable temperature technique.

AMS subject classifications: 52B10, 65D18, 68U05, 68U07

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Key words: Morphological transformation, multi-model scheme, parareal in time simulation.

*Corresponding author.
Email: (L.-P. He), (M. He)

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