An Efficient Rescaling Algorithm for Simulating the Evolution of Multiple Elastically Stressed Precipitates (Communications in Computational Physics, 2013)
In this paper, we propose a space-time rescaling scheme for computing thelong time evolution of multiple precipitates in an elastically stressed medium. Thealgorithm is second order accurate in time, spectrally accurate in space and enablesone to simulate the evolution of precipitates in a fraction of the time normally usedby fixed-frame algorithms. In particular, we extend the algorithm recently developedfor 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. Ourresults show that without elasticity there are successive tip splitting phenomena accompanied by the formation of narrow channels between the precipitates. In presenceof applied elastic field, the precipitates form dendrite-like structures with the primaryarms aligned in the principal directions of the elastic field. We demonstrate that whenthe 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 initialposition of the precipitates, we further observe that some precipitates grow while others may shrink, even when a positive far field flux is applied.