TY - JOUR
T1 - Adaptive mesh computation of polycrystalline pattern formation using a renormalization-group reduction of the phase-field crystal model
AU - Athreya, Badrinarayan P.
AU - Goldenfeld, Nigel
AU - Dantzig, Jonathan A.
AU - Greenwood, Michael
AU - Provatas, Nikolas
PY - 2007/11/16
Y1 - 2007/11/16
N2 - We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field in microscopic material processes. Our numerical approach uses the systematic renormalization-group formulation of a phase-field crystal model of a pure material to provide the underlying equations for the complex amplitude of the atomic density field-a quantity that is spatially uniform except near topological defects, grain boundaries, and other lattice imperfections. Our algorithm employs a hybrid formulation of the amplitude equations, combining Cartesian and polar decompositions of the complex amplitude. We show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline grain growth in two dimensions.
AB - We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field in microscopic material processes. Our numerical approach uses the systematic renormalization-group formulation of a phase-field crystal model of a pure material to provide the underlying equations for the complex amplitude of the atomic density field-a quantity that is spatially uniform except near topological defects, grain boundaries, and other lattice imperfections. Our algorithm employs a hybrid formulation of the amplitude equations, combining Cartesian and polar decompositions of the complex amplitude. We show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline grain growth in two dimensions.
UR - http://www.scopus.com/inward/record.url?scp=36248978164&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=36248978164&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.76.056706
DO - 10.1103/PhysRevE.76.056706
M3 - Article
AN - SCOPUS:36248978164
SN - 1539-3755
VL - 76
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 5
M1 - 056706
ER -