Speaker
Description
The evaluation of electrostatic forces remains a major computational challenge in molecular dynamics (MD) simulations of large-scale systems. Direct pairwise calculations scale as $\mathcal{O}(N^2)$, while long-range interactions under periodic boundary conditions require dedicated algorithms. The current method of choice, Particle Mesh Ewald (PME)[1], achieves $\mathcal{O}(N \log N)$ scaling via fast Fourier transforms; however, its reliance on global communication becomes a bottleneck at very large processor counts.
We present Poisson MaZe[2], a real-space method to compute electrostatic forces within the Mass-Zero constrained dynamics (MaZe) framework[3], developed as a C-based Python package. The method is based on a finite-difference discretization of the Poisson partial differential equation (PDE) for the electrostatic potential, enforced as a dynamical constraint self-consistently coupled to particle dynamics.
The talk addresses three key aspects of the approach. First, we validate the method through realistic simulations of molten NaCl, demonstrating accurate reproduction of structural and transport properties. Second, we examine computational performance: when combined with a multigrid solver, Poisson MaZe achieves linear scaling with system size and converges in substantially fewer cycles than a direct multigrid solution of the Poisson equation. Third, we discuss its numerical properties, including time reversibility, stationarity, conservation of total momentum, and long-time behavior of the energy.
Building on this foundation, we present extensions to implicit-solvent models governed by the Poisson–Boltzmann (PB) equation. To handle the media discontinuities inherent to PB-like models, we employ a numerical treatment analogous to the primal-mixed FEM method. We address the linear case and outline ongoing developments toward nonlinear electrostatic coupling through a field-dependent permittivity $\varepsilon(\mathbf{E})$, with the overarching
goal of improving the electrochemical coupling in the solvent region.
[1] Darden et al., J. Chem. Phys. 98, 10089 (1993).
[2] Troni et al., J. Chem. Phys. 163, 214106 (2025).
[3] Coretti et al., J. Chem. Phys. 157, 214110 (2022).