P3MaZe: a Mass-Zero constrained-dynamics formulation of particle-mesh electrostatics
Abstract
We introduce P3MaZe, a real-space particle-mesh electrostatic method that combines the standard short-range/long-range decomposition of Particle-Particle Particle-Mesh (P3M) electrostatics with the Mass-Zero constrained dynamics (MaZe) framework. In this formulation, the smooth long-range electrostatic potential is represented on a mesh as a zero-inertia auxiliary field, while the discretized Poisson equation is enforced as a holonomic constraint during molecular dynamics. By retaining the standard P3M decomposition, P3MaZe preserves the systematic accuracy controls associated with the real-space cutoff, the Ewald splitting, the mesh spacing, and the charge assignment procedure, while replacing the conventional multigrid Poisson solver by a constrained correction problem. The method is validated for molten NaCl and simple point-charge flexible water (SPC/Fw). Values of the potential, structural, translational, collective, and rotational dynamical observables are in quantitative agreement with those obtained with established electrostatic methods, including real-space P3M, and Ewald summation. We further show that, for the linear, time-independent Poisson operator considered here, the constrained correction problem is algebraically equivalent to a direct Poisson solve initialized by a chronological extrapolation of the mesh potential - a connection not previously established for MaZe-based approaches. This result identifies the precise mechanism through which acceleration of the iterative long-range solve is achieved, and we exploit it systematically through higher-order predictors to further improve convergence, while retaining the expected linear scaling with system size. Because the underlying extrapolation is independent of the constrained-dynamics formalism, it can, of course, also be used directly to accelerate conventional iterative real-space Poisson solvers.
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BibTeX
@misc{troni2026p3maze,
title = {{P3MaZe: a Mass-Zero constrained-dynamics formulation of particle-mesh electrostatics}},
author = {Federica Troni and Violette Gontran and Davide Grassano and Sara Bonella},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.31379},
eprint = {2606.31379},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.31379},
}
RIS
TY - UNPB
TI - P3MaZe: a Mass-Zero constrained-dynamics formulation of particle-mesh electrostatics
AU - Federica Troni
AU - Violette Gontran
AU - Davide Grassano
AU - Sara Bonella
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2606.31379
UR - https://arxiv.org/abs/2606.31379
AB - We introduce P3MaZe, a real-space particle-mesh electrostatic method that combines the standard short-range/long-range decomposition of Particle-Particle Particle-Mesh (P3M) electrostatics with the Mass-Zero constrained dynamics (MaZe) framework. In this formulation, the smooth long-range electrostatic potential is represented on a mesh as a zero-inertia auxiliary field, while the discretized Poisson equation is enforced as a holonomic constraint during molecular dynamics. By retaining the standard P3M decomposition, P3MaZe preserves the systematic accuracy controls associated with the real-space cutoff, the Ewald splitting, the mesh spacing, and the charge assignment procedure, while replacing the conventional multigrid Poisson solver by a constrained correction problem. The method is validated for molten NaCl and simple point-charge flexible water (SPC/Fw). Values of the potential, structural, translational, collective, and rotational dynamical observables are in quantitative agreement with those obtained with established electrostatic methods, including real-space P3M, and Ewald summation. We further show that, for the linear, time-independent Poisson operator considered here, the constrained correction problem is algebraically equivalent to a direct Poisson solve initialized by a chronological extrapolation of the mesh potential - a connection not previously established for MaZe-based approaches. This result identifies the precise mechanism through which acceleration of the iterative long-range solve is achieved, and we exploit it systematically through higher-order predictors to further improve convergence, while retaining the expected linear scaling with system size. Because the underlying extrapolation is independent of the constrained-dynamics formalism, it can, of course, also be used directly to accelerate conventional iterative real-space Poisson solvers.
ER -