An overview of spatial microscopic and accelerated kinetic Monte Carlo methods

被引:366
作者
Chatterjee, Abhijit
Vlachos, Dionisios G. [1 ]
机构
[1] Univ Delaware, Dept Chem Engn, Newark, DE 19716 USA
[2] Univ Delaware, Ctr Catalyt Sci & Technol, Newark, DE 19716 USA
来源
JOURNAL OF COMPUTER-AIDED MATERIALS DESIGN | 2007年 / 14卷 / 02期
基金
美国国家科学基金会;
关键词
review; multiscale simulation; coarse-graining; mesoscopic modeling; Monte Carlo; materials; defects; diffusion; crystal growth; phase transitions; accelerated algorithms; binary tree; efficient update; efficient search; tau-leap; stiff; stochastic; computational singular perturbation; low-dimensional manifold; GRAINED STOCHASTIC-PROCESSES; EMBEDDED-ATOM METHOD; PHASE-TRANSITIONS; SURFACE-DIFFUSION; MULTIRESOLUTION ANALYSIS; STATISTICAL-MECHANICS; THIN-FILMS; TIME-SCALE; AB-INITIO; SIMULATION;
D O I
10.1007/s10820-006-9042-9
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
The microscopic spatial kinetic Monte Carlo (KMC) method has been employed extensively in materials modeling. In this review paper, we focus on different traditional and multiscale KMC algorithms, challenges associated with their implementation, and methods developed to overcome these challenges. In the first part of the paper, we compare the implementation and computational cost of the null-event and rejection-free microscopic KMC algorithms. A firmer and more general foundation of the null-event KMC algorithm is presented. Statistical equivalence between the null-event and rejection-free KMC algorithms is also demonstrated. Implementation and efficiency of various search and update algorithms, which are at the heart of all spatial KMC simulations, are outlined and compared via numerical examples. In the second half of the paper, we review various spatial and temporal multiscale KMC methods, namely, the coarse-grained Monte Carlo (CGMC), the stochastic singular perturbation approximation, and the tau-leap methods, introduced recently to overcome the disparity of length and time scales and the one-at-a time execution of events. The concepts of the CGMC and the tau-leap methods, stochastic closures, multigrid methods, error associated with coarse-graining, a posteriori error estimates for generating spatially adaptive coarse-grained lattices, and computational speed-up upon coarse-graining are illustrated through simple examples from crystal growth, defect dynamics, adsorption-desorption, surface diffusion, and phase transitions.
引用
收藏
页码:253 / 308
页数:56
相关论文
共 149 条
[1]   Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture [J].
Abraham, FF ;
Broughton, JQ ;
Bernstein, N ;
Kaxiras, E .
EUROPHYSICS LETTERS, 1998, 44 (06) :783-787
[2]  
Allen M., 1989, COMPUTER SIMULATION
[3]  
[Anonymous], 1987, Statistical Mechanics: Principles and Selected Applications
[4]   Theory and simulation of jump dynamics, diffusion and phase equilibrium in nanopores [J].
Auerbach, SM .
INTERNATIONAL REVIEWS IN PHYSICAL CHEMISTRY, 2000, 19 (02) :155-198
[5]   R-leaping:: Accelerating the stochastic simulation algorithm by reaction leaps [J].
Auger, Anne ;
Chatelain, Philippe ;
Koumoutsakos, Petros .
JOURNAL OF CHEMICAL PHYSICS, 2006, 125 (08)
[6]   ATOMISTIC MODELING OF MATERIALS PROPERTIES BY MONTE-CARLO SIMULATION [J].
BINDER, K .
ADVANCED MATERIALS, 1992, 4 (09) :540-547
[7]   NEW ALGORITHM FOR MONTE-CARLO SIMULATION OF ISING SPIN SYSTEMS [J].
BORTZ, AB ;
KALOS, MH ;
LEBOWITZ, JL .
JOURNAL OF COMPUTATIONAL PHYSICS, 1975, 17 (01) :10-18
[8]   Applications of molecular modeling in heterogeneous catalysis research [J].
Broadbelt, LJ ;
Snurr, RQ .
APPLIED CATALYSIS A-GENERAL, 2000, 200 (1-2) :23-46
[9]   A multi-scaled approach for simulating chemical reaction systems [J].
Burrage, K ;
Tian, TH ;
Burrage, P .
PROGRESS IN BIOPHYSICS & MOLECULAR BIOLOGY, 2004, 85 (2-3) :217-234
[10]   The slow-scale stochastic simulation algorithm [J].
Cao, Y ;
Gillespie, DT ;
Petzold, LR .
JOURNAL OF CHEMICAL PHYSICS, 2005, 122 (01)