RANDOM BATCH EWALD METHOD FOR DIELECTRICALLY CONFINED COULOMB SYSTEMS

ZC Gan and XZ Gao and JY Liang and ZL Xu, SIAM JOURNAL ON SCIENTIFIC COMPUTING, 47, B846-B874 (2025).

DOI: 10.1137/24M1655809

Quasi two-dimensional (quasi-2D) 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 simulating a collection of N 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 the simulation box, and it achieves optimal \scrO(N) complexity and strong parallel 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 recalibration 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 RBE2D and the particle-particle particle-mesh method (PPPM) is observed, with a significant reduction in the computational cost and improved strong scalability, demonstrating that it is a promising method for a broad range of charged systems under quasi-2D confinement.

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