Multilevel summation for periodic electrostatics using B-splines

Area of Science:

• Computational physics and chemistry
• Scientific computing
• Astrophysical simulations

Background:

• Calculating two-body interactions with periodic boundary conditions is crucial for molecular science and cosmology.
• The 1/r potential presents challenges for energy and force calculations, often addressed by Ewald summation.
• Existing fast methods like fast multipole method (FMM) and particle mesh Ewald (PME) have drawbacks.

Purpose of the Study:

• To introduce and evaluate a novel realization of the multilevel summation method (MSM).
• To demonstrate MSM's advantages over established methods for calculating two-body interactions.
• To present an efficient and scalable computational approach for scientific simulations.

Main Methods:

• Developed a multilevel summation method (MSM) as a multilevel extension of particle mesh Ewald (PME).
• Replaced Ewald softening with a finite-range softening in the MSM realization.
• Implemented and compared a two-level (single-grid) MSM with PME and higher-level MSM versions.

Main Results:

• The two-level MSM requires fewer parameters and is slightly faster than PME.
• Higher-level MSM versions exhibit excellent scalability on large numbers of processors, unlike PME.
• MSM demonstrates greater efficiency than FMM and tree codes for large-scale parallel computations.

Conclusions:

• MSM provides a robust and efficient solution for calculating two-body interactions, overcoming limitations of existing methods.
• MSM offers significant advantages in scalability for parallel computing environments.
• This method enhances the feasibility of large-scale molecular and cosmological simulations.