FFT-based free space Poisson solvers: why Vico-Greengard-Ferrando should replace Hockney-Eastwood

Abstract

Many problems in beam physics and plasma physics require the solution of Poisson's equation with free-space boundary conditions. The algorithm proposed by Hockney and Eastwood is a popular scheme to solve this problem numerically, used by many cutting-edge codes, because of its speed and its simplicity. However, the potential and its gradient obtained with this method have low accuracy, and the numerical error converges slowly with the number of grid points. We demonstrate that the closely related algorithm recently proposed by Vico, Greengard, and Ferrando is just as easy to implement, just as efficient computationally, and has much higher accuracy, with a rapidly converging error.