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Efficient Methods to Compute Long-Range Interactions for Soft Matter Systems

  • Axel ArnoldEmail author
  • Christian Holm
Chapter
Part of the Advances in Polymer Science book series (POLYMER, volume 185)

Abstract

An extensive introduction to the topic of how to compute long-range interactions efficiently is presented. First, the traditional Ewald sum for 3D Coulomb systems is reviewed, then the P3M method of Hockney and Eastwood is discussed in some detail, and alternative ways of dealing with the Coulomb sum are briefly mentioned. The best strategies to perform the sum under partially periodic boundary conditions are discussed, and two recently developed methods are presented, namely the MMM2D and ELC methods for two-dimensionally periodic boundary conditions, and the MMM1D method for systems with only one periodic coordinate. The dipolar Ewald sum is also reviewed. For some of the methods, error formulas are provided which enable the algorithm to be tuned at a predefined accuracy.

Ewald methods Long-range interactions Coulomb sum Periodic boundary conditions Dipolar sum 

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Authors and Affiliations

  1. 1.Max-Planck-Institut für PolymerforschungMainzGermany
  2. 2.Frankfurt Institute for Advanced Studies (FIAS)Johann Wolfgang Goethe-UniversitätFrankfurt/MainGermany

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