A non-periodic particle mesh Ewald method for radially symmetric kernels in free space
Description
The FFT-based smooth particle mesh Ewald (PME) method is extended to non-periodic charge systems interacting via a radially symmetric kernel f(r). The proposed non-periodic PME (NPME) method begins by splitting the kernel f(r) into a short-range component f_s(r) and a smooth long-range component f_l(r). A Fourier extension for f_l(r) is computed numerically using discrete Fourier transform interpolation, enabling efficient treatment of anisotropic rectangular charge volume and offering additional flexibility in the choice of kernel splitting. A derivative-matched (DM) splitting is introduced for general radially symmetric kernels f(r), improving computational performance over traditional Ewald splitting methods. An optimized grid storage algorithm for NPME is proposed, reducing total grid memory by a factor of four. The NPME algorithm is implemented in a C++ library, npme, which supports both pre-defined kernels (e.g. 1/r, r^α, exp(ik_0 r)/r) and user-defined kernels via C++ classes. npme is benchmarked and compared to fmm3D on test systems in computational chemistry and computational electromagnetics. As a practical application, NPME is combined with Method of Moments (MoM) to form a hybrid MoM-NPME algorithm for calculating the radar cross section (RCS) of a perfect electric conductor (PEC). The MoM–NPME method is used to compute the bistatic RCS of a 1-meter PEC sphere at 37.8 GHz and the monostatic RCS of the NASA almond at 75 GHz.