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Multiscale spatial Monte Carlo simulations: multigriding, computational singular perturbation, and hierarchical
Abhijit Chatterjee1, Dionisios G Vlachos
1Department of Chemical Engineering, University of Delaware, Newark, 19716, USA.
The Journal of Chemical Physics
|February 18, 2006
Summary
Two new methods improve coarse-grained Monte Carlo (CGMC) simulations for spatially distributed systems. These approaches enhance accuracy for short-ranged interactions and accelerate computations by coupling fine and coarse grids.
Area of Science:
- Computational Physics
- Materials Science
- Chemical Engineering
Background:
- Traditional Monte Carlo (MC) simulations face challenges with spatially distributed systems due to sequential processing, disparate time scales, and large length scales.
- The recently introduced coarse-grained Monte Carlo (CGMC) method addresses large length scales but relies on a mean-field closure assumption that is inaccurate for short-ranged interactions.
Purpose of the Study:
- To develop improved closure approximations for the CGMC method to enhance accuracy, particularly for systems with short-ranged interactions.
- To introduce computational strategies that accelerate simulations by effectively coupling processes across different length and time scales.
Main Methods:
- Exploration of two novel approaches: the local quasichemical approximation for nearest-neighbor interactions and a multiscale CGMC method utilizing singular perturbation on multiple grids.
- The multiscale CGMC method employs microscopic MC simulations on fine grids to capture cluster probability distributions, leveraging time-scale separation.
- Integration of the binomial tau-leap method with multiscale CGMC to enable parallel processing across the entire lattice, further accelerating computations.
Main Results:
- Both new approaches demonstrate improved accuracy compared to the standard CGMC method, especially in scenarios involving fast diffusion and slow adsorption/desorption processes.
- The multiscale CGMC method, combined with the binomial tau-leap method, provides significant computational acceleration for complex spatially distributed systems.
Conclusions:
- The local quasichemical approximation and the multiscale CGMC method offer more accurate solutions for spatially distributed systems than existing CGMC techniques.
- The developed computational strategies effectively couple different scales, enabling efficient and accurate simulations of systems with multiple, interacting processes.