We present two results: the first is a new method for imposing periodic boundary conditions on unit cells with arbitrary source distributions using the method of images and a low-rank representation based on a plane-wave representation of the fundamental solution. The scheme is insensitive to the unit cell's aspect ratio and easily coupled to adaptive fast multipole methods (FMMs). The second is an acceleration technique for fast Ewald summation, the most widely used approach for computing long-range Coulomb interactions in molecular dynamics (MD) simulations. The resulting method, Ewald summation with prolate spheroidal wave functions (ESP) sharply reduces the size of the Fourier transforms needed in the standard Ewald splitting. We have integrated the ESP method into two widely-used open-source MD packages: LAMMPS and GROMACS, significantly reducing the cost of computing far-field electrostatic interactions.
This is joint work with Shidong Jiang, Jiuyang Liang, Libin Liu, Alex Barnett, Travis Askham and Ruqi Pei.
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