New Splitting Formulations for Lattice Summations
We present a new formulation for the efficient evaluation of pairwise
interactions for large or
spatially periodic infinite lattices. Our
optimally designed splitting
formulation generalizes the Ewald method and its Gaussian core function.
In particular, we show that a polynomial multiplication to the
Gaussian core function can be used to formulate
desired
mathematical or physical characteristics into a
lattice summation method. Two optimization statements are examined:
the first incorporates
a pairwise interaction splitting into the lattice sum, where
the direct (real) and reciprocal space terms also isolate the near-field
andfar-field pairwise particle interactions, respectively; the second
optimization
defines a splitting with a rapidly convergent reciprocal space term that
allows enhanced decay rates in the real-space term relative to the
traditional Ewald method.
The approaches proposed here require modest adaptation to the
Ewald formulation and are expected to enhance
performance of particle-mesh methods for large-scale systems. A
motivation for future applications is large-scale biomolecular
dynamics simulations using particle-mesh Ewald methods and multiple
timestepintegration.
Click to go back to the publication list