The u-series: A separable decomposition for electrostatics computation with improved accuracy.

Area of Science:

• Computational physics
• Materials science
• Biophysics

Background:

• Evaluating electrostatic energy in periodic systems is computationally intensive due to the long-range Coulomb interaction.
• Standard methods like Ewald decomposition involve approximations, balancing accuracy and performance.
• New decomposition techniques are sought for improved trade-offs in molecular dynamics simulations.

Purpose of the Study:

• To present the u-series, a novel decomposition of the Coulomb potential.
• To demonstrate its improved accuracy and computational efficiency over the standard Ewald decomposition.
• To explore performance enhancements on modern parallel supercomputers.

Main Methods:

• Decomposition of the Coulomb potential into near and far parts.
• Direct summation for the near part up to a cutoff radius.
• Fourier space evaluation for the far part, utilizing a sum of Gaussians for the u-series.
• Numerical validation using a lipid membrane system.

Main Results:

• The u-series achieves higher accuracy than the Ewald decomposition for equivalent computational effort.
• The u-series matches Ewald's accuracy with approximately half the computational cost.
• The Gaussian nature of the u-series' far part enables specialized algorithms for performance gains.

Conclusions:

• The u-series offers a more accurate and computationally efficient method for electrostatic energy evaluation.
• Its properties allow for optimized algorithms, particularly beneficial for massively parallel computing.
• This method presents a significant advancement for molecular dynamics and related simulations.