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Manuscript Title: GMIC++: grouping method in C++: an efficient method to solve a large number of master equations.
Authors: A.M. Ovcharenko, S.I. Golubov, C.H. Woo, H. Huang
Program title: GMIC++
Catalogue identifier: ADRK_v1_0
Distribution format: zip
Journal reference: Comput. Phys. Commun. 152(2003)208
Programming language: C++.
Computer: PC Pentium III.
Operating system: Windows NT/2000/XP, Cygwin, Linux Red Hat v8.0.
RAM: 500K words
Keywords: Grouping method, Master equation, Nucleation, Growth, Clusters, Molecular physics, Chemical kinetics, Statistical physics, Thermodynamics.
Classification: 16.12, 23.

Nature of problem:
A common approach to describe defect/adatom accumulation processes is by using a system of master equations. For a good description, the number of equations in the system is generally very large. As a result, their numerical solution is very time consuming. This problem is less serious at the early stage. However, as the process continues, the number of master equations increases and the numerical difficulty becomes severe.

Solution method:
To physically track the details of the accumulation process with available computational resources, Kiritani [1] first proposed the group method. Accordingly, the system of master equations is divided into groups, keeping the first moments unchanged. Realizing the inadequacy of the original grouping method, Golubov et al [2] proposed to preserve also the second moment, which has been shown to provide an accurate description of the defect/adatom accumulation processes, as originally described by a large number of master equations.

The method is valid for general defect/adatom accumulation processes, which are describable by a set of master equations.

Running time:
It depends on energetics and the speed of the processes involved. As an example, it takes 30 seconds on a Pentium III processor at 1GHz clock frequency to track the vacancy clustering in nickel during one hour ageing at 550oC, solving a system of up to 300 master equations.

[1] M. Kiritani, J. Phys. Soc. Japan 37 (1974) 1532.
[2] S.I. Golubov, A.M. Ovcharenko, A.V. Barashev and B.N. Singh, Phil. Mag. A 81 (2001) 643.