Random Batch Ewald Method for Dielectrically Confined Coulomb Systems

Fuente: arXiv
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Main Authors: Gan, Zecheng, Gao, Xuanzhao, Liang, Jiuyang, Xu, Zhenli
Format: Preprint
Published: 2024
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_version_ 1866908448400080896
author Gan, Zecheng
Gao, Xuanzhao
Liang, Jiuyang
Xu, Zhenli
author_facet Gan, Zecheng
Gao, Xuanzhao
Liang, Jiuyang
Xu, Zhenli
contents Quasi two-dimensional Coulomb systems have drawn widespread interest. The reduced symmetry of these systems leads to complex collective behaviors, yet simultaneously poses significant challenges for particle-based simulations. In this paper, a novel method is presented for efficiently simulate a collection of charges confined in doubly-periodic slabs, with the extension to scenarios involving dielectric jumps at slab boundaries. Unlike existing methods, the method is insensitive to the aspect ratio of simulation box, and it achieves optimal O(N) complexity and strong scalability, thanks to the random batch Ewald (RBE) approach. Moreover, the additional cost for polarization contributions, represented as image reflection series, is reduced to a negligible cost via combining the RBE with an efficient structure factor coefficient re-calibration technique in k-space. Explicit formulas for optimal parameter choices of the algorithm are provided through error estimates, together with a rigorous proof. Finally, we demonstrate the accuracy, efficiency and scalability of our method, called RBE2D, via numerical tests across a variety of prototype systems. An excellent agreement between the RBE2D and the PPPM method is observed, with a significant reduction in the computational cost and strong scalability, demonstrating that it is a promising method for a broad range of charged systems under quasi-2D confinement.
format Preprint
id arxiv_https___arxiv_org_abs_2405_06333
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Random Batch Ewald Method for Dielectrically Confined Coulomb Systems
Gan, Zecheng
Gao, Xuanzhao
Liang, Jiuyang
Xu, Zhenli
Numerical Analysis
82M37, 65C35, 65T50, 65Y05
Quasi two-dimensional Coulomb systems have drawn widespread interest. The reduced symmetry of these systems leads to complex collective behaviors, yet simultaneously poses significant challenges for particle-based simulations. In this paper, a novel method is presented for efficiently simulate a collection of charges confined in doubly-periodic slabs, with the extension to scenarios involving dielectric jumps at slab boundaries. Unlike existing methods, the method is insensitive to the aspect ratio of simulation box, and it achieves optimal O(N) complexity and strong scalability, thanks to the random batch Ewald (RBE) approach. Moreover, the additional cost for polarization contributions, represented as image reflection series, is reduced to a negligible cost via combining the RBE with an efficient structure factor coefficient re-calibration technique in k-space. Explicit formulas for optimal parameter choices of the algorithm are provided through error estimates, together with a rigorous proof. Finally, we demonstrate the accuracy, efficiency and scalability of our method, called RBE2D, via numerical tests across a variety of prototype systems. An excellent agreement between the RBE2D and the PPPM method is observed, with a significant reduction in the computational cost and strong scalability, demonstrating that it is a promising method for a broad range of charged systems under quasi-2D confinement.
title Random Batch Ewald Method for Dielectrically Confined Coulomb Systems
topic Numerical Analysis
82M37, 65C35, 65T50, 65Y05
url https://arxiv.org/abs/2405.06333