Arno Leist

Parallel graph component labelling with GPUs and CUDA

Graph component labelling, which is a subset of the general graph colouring problem, is a computationally expensive operation that is of importance in many applications and simulations. A number of data-parallel algorithmic variations to the component labelling problem are possible and we explore their use with general purpose graphical processing units (GPGPUs) and with the CUDA GPU programming language. We discuss implementation issues and performance results on GPUs using CUDA. We present results for regular mesh graphs as well as arbitrary structured and topical graphs such as small-world and scale-free structures. We show how different algorithmic variations can be used to best effect depending upon the cluster structure of the graph being labelled and consider how features of the GPU architectures and host CPUs can be combined to best effect into a cluster component labelling algorithm for use in high performance simulations.

Regular Lattice and Small-World Spin Model Simulations Using CUDA and GPUs

Data-parallel accelerator devices such as Graphical Processing Units (GPUs) are providing dramatic performance improvements over even multi-core CPUs for lattice-oriented applications in computational physics. Models such as the Ising and Potts models continue to play a role in investigating phase transitions on small-world and scale-free graph structures. These models are particularly well-suited to the performance gains possible using GPUs and relatively high-level device programming languages such as NVIDIA’s Compute Unified Device Architecture (CUDA). We report on algorithms and CUDA data-parallel programming techniques for implementing Metropolis Monte Carlo updates for the Ising model using bit-packing storage, and adjacency neighbour lists for various graph structures in addition to regular hypercubic lattices. We report on parallel performance gains and also memory and performance tradeoffs using GPU/CPU and algorithmic combinations.

Interactive visualisation of spins and clusters in regular and small-world Ising models with CUDA on GPUs

Abstract Three-dimensional simulation models are hard to visualise for dense lattice systems, even with cutaways and flythrough techniques. We use multiple Graphics Processing Units (GPUs), CUDA and OpenGL to increase our understanding of computational simulation models such as the 2-D and 3-D Ising systems with small-world link rewiring by accelerating both the simulation and visualisation into interactive time. We show how interactive model parameter updates, visual overlaying of measurements and graticules, cluster labelling and other visual highlighting cues enhance user intuition of the model’s meaning and exploit the enhanced simulation speed to handle model systems large enough to explore multi-scale phenomena.

Comparing Intra- and Inter-Processor Parallelism on Multi-Core CellBE Processors for Scientific Simulations

The Cell Broadband Engine (Cell BE) multi-core processor from the STI consortium of Sony, Toshiba and IBM is a powerful but complex processing device that has attracted much attention since its inclusion in Sony PlayStation (PS3) gaming consoles. We report on some performance experiments using the multicore Synergistic Processing Elements (SPE) concurrency capabilities of this chip. We compare performance and software implementation issues with conventional cluster computing techniques such as message-passing, in exploiting clusters of Cell BE processors for scientific simulations. We discuss performance and user programming issues for some hybrid solutions on clustered PS3 computers running Linux.

Visualising spins and clusters in regular and small-world Ising models with GPUs

Abstract Visualising computational simulation models of solid state physical systems is a hard problem for dense lattice models. Fly-throughs and cutaways can aid viewer understanding of a simulated system. Interactive time model parameter updates and overlaying of measurements and graticules, cluster colour labelling and other visual highlighting cues can also enhance user intuition of the model’s meaning. We present some graphical and simulation optimisation techniques and various graphical rendering and explanatory techniques for computational simulation models such as the Ising model in 2 and 3 dimensions. In addition to aiding understanding of conventional algorithms such as Metropolis Monte Carlo, we try to visualise cluster updates to the system using algorithms like that of Wolff. We also explore ways to visualise path-length shortening and other changes to the Ising system when small-world link rewiring is applied to the system. We use a combination of OpenGL visualisation software and General Purpose Computing on Graphics Processing Units (GPGPU) with the Compute Unified Device Architecture (CUDA) and consider ways to accelerate both the simulation itself as well as the graphical rendering to make an interactive system of model system sizes that are large enough to be challenging and visually interesting.

Visualising Volumetric Fourier Transforms of Asymmetric 3D Growth Models

Volumetric visualisation of Fourier spectral data is a powerful but computationally intensive tool for understanding growth models. Visualising frequency-domain spectral representations of simulation model variables that are normally defined on a spatial mesh can be a useful aid to understanding time evolutionary behaviour. While it is common to study the symmetric or spherically averaged FFT of models, we consider rendering the full 3D FFT representations in interactive time. We use volume rendering methods to study the FFT and also consider asymmetric model cases where spherical averaging would be misleading. We discuss visualisation of Fourier-transformed data fields and some techniques for analysing and interpreting them. We present some application examples and implementations of rendering iso surfaces in the spectral scattering representation of of the normal and small-world rewired Ising model using Graphical Processing Units(GPUs) that allow both simulation and rendering to be achieved in interactive time.