A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensions

摘要

An efficient solver for the three dimensional free-space Poisson equation ispresented. The underlying numerical method is based on finite Fourier seriesapproximation. While the error of all involved approximations can be fullycontrolled, the overall computation error is driven by the convergence of thefinite Fourier series of the density. For smooth and fast-decaying densitiesthe proposed method will be spectral accurate. The method scales with$\mathcal{O}(N\log N)$ operations, where $N$ is the total number ofdiscretization points in the Cartesian grid. The majority of the computationalcosts come from fast Fourier transforms (FFT), which makes it ideal for GPUcomputation. Several numerical computations on CPU and GPU validate the methodand show efficiency and convergence behavior. Tests are performed using theVienna Scientific Cluster 3 (VSC3). A free MATLAB implementation for CPU andGPU is provided to the interested community.