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An Efficient Rescaling Algorithm for Simulating the Evolution of Multiple Elastically Stressed Precipitates

Published online by Cambridge University Press:  03 June 2015

Amlan K. Barua ,
Shuwang Li ,
Hualong Feng ,
Xiaofan Li  and
John Lowengrub
Amlan K. Barua*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, USA
Shuwang Li*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, USA
Hualong Feng*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, USA
Xiaofan Li*
Affiliation:
Department of Applied Mathematics, Illinois Institute of Technology, Chicago 60616, USA
John Lowengrub*
Affiliation:
Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA
*
Email:abarua@iit.edu
Corresponding author.Email:sli@math.iit.edu
Email:hfeng@iit.edu
Email:lix@iit.edu
Email:lowengrb@math.uci.edu
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Abstract

In this paper, we propose a space-time rescaling scheme for computing the long time evolution of multiple precipitates in an elastically stressed medium. The algorithm is second order accurate in time, spectrally accurate in space and enables one to simulate the evolution of precipitates in a fraction of the time normally used by fixed-frame algorithms. In particular, we extend the algorithm recently developed for single particle by Li et al. (Li, Lowengrub and Leo, J. Comput. Phys., 335 (2007), 554) to the multiple particle case, which involves key differences in the method. Our results show that without elasticity there are successive tip splitting phenomena accompanied by the formation of narrow channels between the precipitates. In presence of applied elastic field, the precipitates form dendrite-like structures with the primary arms aligned in the principal directions of the elastic field. We demonstrate that when the far-field flux decreases with the effective radius of the system, tip-splitting and dendrite formation can be suppressed, as in the one particle case. Depending on the initial position of the precipitates, we further observe that some precipitates grow while others may shrink, even when a positive far field flux is applied.

Keywords

74N2574B15Diffusionelasticitydendriteside branchingboundary integral method

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Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 4 , October 2013 , pp. 940 - 959
Copyright
Copyright © Global Science Press Limited 2013

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