TY - JOUR
T1 - An Efficient Adaptive Rescaling Scheme for Computing Moving Interface Problems
AU - Meng Zhao, Wenjun Ying, John Lowengrub & Shuwang Li
JO - Communications in Computational Physics
VL - 3
SP - 679
EP - 691
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.OA-2016-0040
UR - https://global-sci.org/intro/article_detail/cicp/11255.html
KW - 
AB - <p style="text-align: justify;">In this paper, we present an efficient rescaling scheme for computing the
long-time dynamics of expanding interfaces. The idea is to design an adaptive time-space
mapping such that in the new time scale, the interfaces evolves logarithmically
fast at early growth stage and exponentially fast at later times. The new spatial scale
guarantees the conservation of the area/volume enclosed by the interface. Compared
with the original rescaling method in [J. Comput. Phys. 225(1) (2007) 554–567], this
adaptive scheme dramatically improves the slow evolution at early times when the
size of the interface is small. Our results show that the original three-week computation
in [J. Comput. Phys. 225(1) (2007) 554–567] can be reproduced in about one
day using the adaptive scheme. We then present the largest and most complicated
Hele-Shaw simulation up to date.</p>