12ème JEAN, 18 décembre 2014
Yong Zhang
:
Accurate and efficient computation of some
nonlocal potentials based on Gaussian-sum approximation
We introduce an accurate and efficient method for the evaluation of a class of free space nonlocal potentials, such as the free space Coulomb and Poisson potential in 2D/3D and dipolar potential in 2D/3D. Starting from the convolution formulation, for smooth and fast decaying densities, we make a full use of the Fourier pesudospectral (plane wave) approximation of the density and a separable Gaussian sums approximation of the kernel in an interval where the singularity point (the origin) is excluded. Hence, the potential is split into a regular integral and a correction integral, and the latter is well resolved utilising a low-order Taylor expansion of the density. Both can be computed with fast Fourier transforms (FFT). The method is accurate (14-16 digits), efficient (\(O(N \log N\)) complexity), low in storage, easily adaptable to other different kernels, applicable for anisotropic densities and highly parallelable.
