English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The evaluation of long-range potentials in periodic, many-body systems arisesas a necessary step in the numerical modeling of a multitude of interestingphysical problems. Direct evaluation of these potentials requires O(N^2)operations and O(N^2) storage, where N is the number of interacting bodies. Inthis work, we present a method, which requires O(N) operations and O(N)storage, for the evaluation of periodic Helmholtz, Coulomb, and Yukawapotentials with periodicity in 1-, 2-, and 3-dimensions, using the method ofAccelerated Cartesian Expansions (ACE). We present all aspects necessary toeffect this acceleration within the framework of ACE including the necessarytranslation operators, and appropriately modifying the hierarchicalcomputational algorithm. We also present several results that validate theefficacy of this method with respect to both error convergence and costscaling, and derive error bounds for one exemplary potential.

An O(N) Method for Rapidly Computing Periodic Potentials Using Accelerated Cartesian Expansions