Optimizing kernel methods for Poisson integrals on a uniform grid

We analyze the error and error propagation in the calculation of the Poisson integral on a uniform grid within Density Functional Theory (DFT) real-space calculations. We suggest and examine several schemes for near neighbors' interaction correction for the Green's function kernel to improve the accuracy. Finally, we demonstrate the effect of the different kernels on DFT eigenvalues and Hartree energy accuracy in systems such as C60 and C40H82.