A hierarchical algorithm for fast Debye summation with applications to small angle scattering.

ABSTRACT: Debye summation, which involves the summation of sinc functions of distances between all pair of atoms in three-dimensional space, arises in computations performed in crystallography, small/wide angle X-ray scattering (SAXS/WAXS), and small angle neutron scattering (SANS). Direct evaluation of Debye summation has quadratic complexity, which results in computational bottleneck when determining crystal properties, or running structure refinement protocols that involve SAXS or SANS, even for moderately sized molecules. We present a fast approximation algorithm that efficiently computes the summation to any prescribed accuracy ε in linear time. The algorithm is similar to the fast multipole method (FMM), and is based on a hierarchical spatial decomposition of the molecule coupled with local ha

SUBMITTER: Gumerov NA 

PROVIDER: S-EPMC3425727 | biostudies-literature | 2012 Sep

REPOSITORIES: biostudies-literature