Lattice boltzmann based PDE solver on the GPU

In this paper, we propose a hardware-accelerated PDE (partial differential equation) solver based on the lattice Boltzmann model (LBM). The LBM is initially designed to solve fluid dynamics by constructing simplified microscopic kinetic models. As an explicit numerical scheme with only local operations, it has the advantage of being easy to implement and especially suitable for graphics hardware (GPU) acceleration. Beyond the Navier-Stokes equation of fluid mechanics, a typical LBM can be modified to solve the parabolic diffusion equation, which is further used to solve the elliptic Laplace and Poisson equations with a diffusion process. These PDEs are widely used in modeling and manipulating images, surfaces and volumetric data sets. Therefore, the LBM scheme can be used as an GPU-based numerical solver to provide a fast and convenient alternative to traditional implicit iterative solvers. We apply this method to several examples in volume smoothing, surface fairing and image editing, achieving outstanding performance on contemporary graphics hardware. It has the great potential to be used as a general GPU computing framework for efficiently solving PDEs in image processing, computer graphics and visualization.