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

Abstract

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

References in corpus (4)

• Efficient solution of Poisson's equation with free boundary conditions
• Efficient and accurate three dimensional Poisson solver for surface problems
• Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation
• Parallel FFT-based Poisson Solver for Isolated Three-dimensional Systems

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