@Article{CiCP-14-940,
author = {},
title = {An Efficient Rescaling Algorithm for Simulating the Evolution of Multiple Elastically Stressed Precipitates},
journal = {Communications in Computational Physics},
year = {2013},
volume = {14},
number = {4},
pages = {940--959},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.251012.271212a},
url = {http://global-sci.org/intro/article_detail/cicp/7187.html}
}