How to mesh up Ewald sums. II. An accurate error estimate for the particle–particle–particle-mesh algorithm

1998/07/07 by Markus Deserno, Christian Holm · 363 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Computer science #Construct (python library) #Data mining #Electromagnetic Scattering and Analysis #Function (biology) #High-Energy Particle Collisions Research #Mathematics #Mean squared error #Measure (data warehouse) #Particle (ecology) #Particle system #Probabilistic and Robust Engineering Design #Statistics #cond-mat.soft

paper · pdf · doi:10.1063/1.477415

published in The Journal of Chemical Physics 109(18), 7694-7701 (American Institute of Physics) · 9 pages, 7 figures included, revtex style

arxiv created 1998/07/07 · openalex publication_date 1998/11/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We construct an accurate estimate for the root mean square force error of the particle–particle–particle mesh (P3M) algorithm by extending a single particle pair error measure which has been given by Hockney and Eastwood. We also derive an easy to use analytic approximation to the error formula. This allows a straightforward and precise determination of the optimal splitting parameter (as a function of system specifications and P3M parameters) and hence knowledge of the force accuracy prior to the actual simulation. The high quality of the estimate is demonstrated in several examples.

Citations

• Die Berechnung optischer und elektrostatischer Gitterpotentiale
• Accuracy and efficiency of the particle mesh Ewald method

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