Accelerating population balanceMonte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing
Abstract
This paper proposes a comprehensive framework for accelerating population balanceMonte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulationrule matrix of differentiallyweighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the twoparticle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by singlelooping over all particles, and meanwhile the mean timestep of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentiallyweighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number ofmore »
 Authors:
 Publication Date:
 OSTI Identifier:
 22382171
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Computational Physics; Journal Volume: 281; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ALGORITHMS; BENCHMARKS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; GAIN; KERNELS; MARKOV PROCESS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; MATRICES; MONTE CARLO METHOD; PARTICLE SIZE
Citation Formats
Xu, Zuwei, Zhao, Haibo, Email: klinsmannzhb@163.com, and Zheng, Chuguang. Accelerating population balanceMonte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.10.055.
Xu, Zuwei, Zhao, Haibo, Email: klinsmannzhb@163.com, & Zheng, Chuguang. Accelerating population balanceMonte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing. United States. doi:10.1016/J.JCP.2014.10.055.
Xu, Zuwei, Zhao, Haibo, Email: klinsmannzhb@163.com, and Zheng, Chuguang. 2015.
"Accelerating population balanceMonte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing". United States.
doi:10.1016/J.JCP.2014.10.055.
@article{osti_22382171,
title = {Accelerating population balanceMonte Carlo simulation for coagulation dynamics from the Markov jump model, stochastic algorithm and GPU parallel computing},
author = {Xu, Zuwei and Zhao, Haibo, Email: klinsmannzhb@163.com and Zheng, Chuguang},
abstractNote = {This paper proposes a comprehensive framework for accelerating population balanceMonte Carlo (PBMC) simulation of particle coagulation dynamics. By combining Markov jump model, weighted majorant kernel and GPU (graphics processing unit) parallel computing, a significant gain in computational efficiency is achieved. The Markov jump model constructs a coagulationrule matrix of differentiallyweighted simulation particles, so as to capture the time evolution of particle size distribution with low statistical noise over the full size range and as far as possible to reduce the number of time loopings. Here three coagulation rules are highlighted and it is found that constructing appropriate coagulation rule provides a route to attain the compromise between accuracy and cost of PBMC methods. Further, in order to avoid double looping over all simulation particles when considering the twoparticle events (typically, particle coagulation), the weighted majorant kernel is introduced to estimate the maximum coagulation rates being used for acceptance–rejection processes by singlelooping over all particles, and meanwhile the mean timestep of coagulation event is estimated by summing the coagulation kernels of rejected and accepted particle pairs. The computational load of these fast differentiallyweighted PBMC simulations (based on the Markov jump model) is reduced greatly to be proportional to the number of simulation particles in a zerodimensional system (single cell). Finally, for a spatially inhomogeneous multidimensional (multicell) simulation, the proposed fast PBMC is performed in each cell, and multiple cells are parallel processed by multicores on a GPU that can implement the massively threaded dataparallel tasks to obtain remarkable speedup ratio (comparing with CPU computation, the speedup ratio of GPU parallel computing is as high as 200 in a case of 100 cells with 10 000 simulation particles per cell). These accelerating approaches of PBMC are demonstrated in a physically realistic Brownian coagulation case. The computational accuracy is validated with benchmark solution of discretesectional method. The simulation results show that the comprehensive approach can attain very favorable improvement in cost without sacrificing computational accuracy.},
doi = {10.1016/J.JCP.2014.10.055},
journal = {Journal of Computational Physics},
number = ,
volume = 281,
place = {United States},
year = 2015,
month = 1
}

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