Fast Algorithm for Quasi-2D Coulomb Systems
arxiv(2024)
摘要
Quasi-2D Coulomb systems are of fundamental importance and have attracted
much attention in many areas nowadays. Their reduced symmetry gives rise to
interesting collective behaviors, but also brings great challenges for
particle-based simulations. Here, we propose a novel algorithm framework to
address the 𝒪(N^2) simulation complexity associated with the
long-range nature of Coulomb interactions. First, we introduce an efficient
Sum-of-Exponentials (SOE) approximation for the long-range kernel associated
with Ewald splitting, achieving uniform convergence in terms of inter-particle
distance, which reduces the complexity to 𝒪(N^7/5). We then
introduce a random batch sampling method in the periodic dimensions, the
stochastic approximation is proven to be both unbiased and with reduced
variance via a tailored importance sampling strategy, further reducing the
computational cost to 𝒪(N). The performance of our algorithm is
demonstrated via varies numerical examples. Notably, it achieves a speedup of
2∼ 3 orders of magnitude comparing with Ewald2D method, enabling molecular
dynamics (MD) simulations with up to 10^6 particles on a single core. The
present approach is therefore well-suited for large-scale particle-based
simulations of Coulomb systems under confinement, making it possible to
investigate the role of Coulomb interaction in many practical situations.
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