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Efficient implementation of the Barnes-Hut octree algorithm for Monte Carlo simulations of charged systems

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Abstract

Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many biological and soft matter materials solvable in solvents. The appropriate treatment of long-range electrostatic interaction is essential for these charged systems, but remains a challenging problem for large-scale simulations. We have developed an efficient Barnes-Hut treecode algorithm for electrostatic evaluation in Monte Carlo simulations of Coulomb many-body systems. The algorithm is based on a divideand-conquer strategy and fast update of the octree data structure in each trial move through a local adjustment procedure. We test the accuracy of the tree algorithm, and use it to perform computer simulations of electric double layer near a spherical interface. It has been shown that the computational cost of the Monte Carlo method with treecode acceleration scales as log N in each move. For a typical system with ten thousand particles, by using the new algorithm, the speed has been improved by two orders of magnitude from the direct summation.

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Authors and Affiliations

  1. Department of Mathematics, Institute of Natural Sciences, and MoE Key Lab of Scientific and Engineering Computing, Shanghai Jiao Tong University, Shanghai, 200240, China

    ZeCheng Gan & ZhenLi Xu

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  1. ZeCheng Gan
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  2. ZhenLi Xu
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Correspondence to ZhenLi Xu.

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Gan, Z., Xu, Z. Efficient implementation of the Barnes-Hut octree algorithm for Monte Carlo simulations of charged systems. Sci. China Math. 57, 1331–1340 (2014). https://doi.org/10.1007/s11425-014-4783-5

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  • DOI: https://doi.org/10.1007/s11425-014-4783-5

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