dorsal/arxiv
View SchemaAn $O(\log N)$ Monte Carlo method for periodic Coulomb systems
| Authors | Xuanzhao Gao, Shidong Jiang, Jiuyang Liang, Qi Zhou |
|---|---|
| Categories | |
| ArXiv ID | 2601.09288vv1 |
| URL | https://arxiv.org/abs/2601.09288 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
Efficient Monte Carlo (MC) sampling of many-body systems with long-range electrostatics is often limited by the cost of per-move energy-difference evaluation under periodic boundary conditions. We present DMK-MC, an accelerated MC method that adapts the dual-space multilevel kernel-splitting (DMK) framework to single-particle Metropolis updates. DMK-MC computes the energy change and, upon acceptance, updates the stored incoming plane-wave fields with $O(1)$ work per tree level, yielding an overall $O(\log N)$ expected work per trial move for fixed accuracy. The method decomposes the Coulomb kernel into three components: a global, periodized smooth part; a multilevel sequence of smooth difference kernels whose interactions are restricted to same-level colleague boxes; and a singular residual kernel whose short-range interactions are evaluated directly. Benchmarks on uniform, highly nonuniform, and implicit-solvent electrolyte and colloidal configurations show that DMK-MC consistently outperforms a recent FMM-based $O(\log N)$ Monte Carlo method, delivering several-fold speedups at comparable tolerances.
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"abstract": "Efficient Monte Carlo (MC) sampling of many-body systems with long-range electrostatics is often limited by the cost of per-move energy-difference evaluation under periodic boundary conditions. We present DMK-MC, an accelerated MC method that adapts the dual-space multilevel kernel-splitting (DMK) framework to single-particle Metropolis updates. DMK-MC computes the energy change and, upon acceptance, updates the stored incoming plane-wave fields with $O(1)$ work per tree level, yielding an overall $O(\\log N)$ expected work per trial move for fixed accuracy. The method decomposes the Coulomb kernel into three components: a global, periodized smooth part; a multilevel sequence of smooth difference kernels whose interactions are restricted to same-level colleague boxes; and a singular residual kernel whose short-range interactions are evaluated directly. Benchmarks on uniform, highly nonuniform, and implicit-solvent electrolyte and colloidal configurations show that DMK-MC consistently outperforms a recent FMM-based $O(\\log N)$ Monte Carlo method, delivering several-fold speedups at comparable tolerances.",
"arxiv_id": "2601.09288",
"authors": [
"Xuanzhao Gao",
"Shidong Jiang",
"Jiuyang Liang",
"Qi Zhou"
],
"categories": [
"physics.comp-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "An $O(\\log N)$ Monte Carlo method for periodic Coulomb systems",
"url": "https://arxiv.org/abs/2601.09288",
"version": "v1"
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