A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensions
- Author(s)
- Lukas Exl
- 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 spectrally accurate. The method scales with O(NlogN) 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. Program summary Program Title: GSPoisson3d Program Files doi: dx.doi.org/10.17632/xh6d47sxx8.1 Licensing provisions: MIT Programming language: MATLAB R2015b Nature of problem: Efficient and accurate computation of the unbounded Poisson equation in three dimensions. Solution method: Fourier based approach with Gaussian-sum approximation of the singular convolution kernel and near field correction — both utilizing FFT. Additional comments: Incorporated GPU acceleration via MATLAB's GPU fft implementation.
- Organisation(s)
- Physics of Functional Materials, Department of Mathematics
- Journal
- Computer Physics Communications
- Volume
- 221
- Pages
- 352-357
- No. of pages
- 6
- ISSN
- 0010-4655
- DOI
- https://doi.org/10.1016/j.cpc.2017.08.014
- Publication date
- 12-2017
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101014 Numerical mathematics
- Keywords
- ASJC Scopus subject areas
- Physics and Astronomy(all), Hardware and Architecture
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/a-gpu-accelerated-and-errorcontrolled-solver-for-the-unbounded-poisson-equation-in-three-dimensions(41ff42c5-bb44-463d-874f-77bbc3c97c98).html