Daniel P. Playne

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.

Comparison of GPU architectures for asynchronous communication with finite-differencing applications

Graphical processing units (GPUs) are good data‐parallel performance accelerators for solving regular mesh partial differential equations (PDEs) whereby low‐latency communications and high compute to communications ratios can yield very high levels of computational efficiency. Finite‐difference time‐domain methods still play an important role for many PDE applications. Iterative multi‐grid and multilevel algorithms can converge faster than ordinary finite‐difference methods but can be much more difficult to parallelize with GPU memory constraints. We report on some practical algorithmic and data layout approaches and on performance data on a range of GPUs with CUDA. We focus on the use of multiple GPU devices with a single CPU host and the asynchronous CPU/GPU communications issues involved. We obtain more than two orders of magnitude of speedup over a comparable CPU core. Copyright

Hypercubic storage layout and transforms in arbitrary dimensions using GPUs and CUDA

Many simulations in the physical sciences are expressed in terms of rectilinear arrays of variables. It is attractive to develop such simulations for use in 1‐, 2‐, 3‐ or arbitrary physical dimensions and also in a manner that supports exploitation of data‐parallelism on fast modern processing devices. We report on data layouts and transformation algorithms that support both conventional and data‐parallel memory layouts. We present our implementations expressed in both conventional serial C code as well as in NVIDIAs Compute Unified Device Architecture concurrent programming language for use on general purpose graphical processing units. We discuss: general memory layouts; specific optimizations possible for dimensions that are powers‐of‐two and common transformations, such as inverting, shifting and crinkling. We present performance data for some illustrative scientific applications of these layouts and transforms using several current GPU devices and discuss the code and speed scalability of this approach. Copyright

Modelling, simulating and visualising the Cahn-Hilliard-Cook field equation

The Cahn-Hilliard-Cook equation continues to be a useful model describing binary phase separation in systems such as alloys and other physical and chemical applications. We describe our investigation of this field equation and report on the various discretisation schemes we used to integrate the system in one-, two- and three-dimensions. We also discuss how the equation can be visualised effectively in these different dimensions and consider how these techniques can usefully be applied to other partial differential equations.

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.

Automated and parallel code generation for finite-differencing stencils with arbitrary data types

Abstract Finite-Differencing and other regular and direct approaches to solving partial differential equations (PDEs) are methods that fit well on data-parallel computer systems. These problems continue to arise in many application areas of computational science and engineering but still offer some programming challenges as they are not readily incorporated into a general standard software library that could cover all possible PDEs. Achieving high performance on numerical solutions to PDEs generally requires exposure of the field data structures and application of knowledge of how best to map them to the memory and processing architecture of a particular parallel computer system. Stencil methods for solving PDEs are however readily implemented as semi-automatically generated skeletal frameworks. We have implemented semi-automated stencil source code generators for a number of target programming languages including data-parallel languages such as CUDA for graphics processing units (GPUs). We report on some performance evaluations for our generated PDE simulations on GPUs and other platforms. In this article we focus on (diffusive) PDEs with a non-trivial data type requirement such as having vector or complex field variables. We discuss the issues and compromises involved implementing equation solvers with fields comprising arbitrary data types on GPUs and other current compute devices.

Asynchronous Communication Schemes for Finite Difference Methods on Multiple GPUs

Finite difference methods continue to provide an important and parallelisable approach to many numerical simulations problems. Iterative multigrid and multilevel algorithms can converge faster than ordinary finite difference methods but can be more difficult to parallelise. Data parallel paradigms tend to lend themselves particularly well to solving regular mesh PDEs whereby low latency communications and high compute to communications ratios can yield high levels of computational efficiency and raw performance. We report on some practical algorithmic and data layout approaches and on performance data on a range of Graphical Processing Units (GPUs) with CUDA. We focus on the use of multiple GPU devices with a single CPU host.

Knowledge-based role allocation in robot soccer

Robot soccer teams consist of a number of robots each performing a different role within the team. The roles discussed in this paper are: goalie, defender, attacker, supporter and centre. These roles are too often statically assigned to the robots at the start of the game. Knowledge-based techniques can be used to assign these roles dynamically to allow the team to adopt the optimal behaviour for each situation. Dynamic strategy choice can also be implemented within the same knowledge-based system. A strategy (defend or attack) can be chosen based on robot and ball location which in turn determines which roles should be used in play. Once the roles are defined, they will be assigned to the best robot for each role in turn based on role importance. Testing within the Teambot simulator shows a significant in score and ball control dominance over the same team with static role allocation. This paper presents the knowledge-based role assignment approach employed and the favourable results obtained.

Hybrid Fuzzy Colour Processing and Learning

We present a robust fuzzy colour processing system with automatic rule extraction and colour descriptors calibration for accurate colour object recognition and tracking in real-time. The system is anchored on the fusion of fuzzy colour contrast rules that operate on the red, green and blue channels independently and adaptively to compensate for the effects of glare, shadow, and illumination variations in an indoor environment. The system also utilises a pie-slice colour classification technique in a modified rg-chromaticity space. Now, colour operations can be defined linguistically to allow a vision system to discriminate between similarly coloured objects more effectively. The validity and generality of the proposed fuzzy colour processing system is analysed by examining the complete mapping of the fuzzy colour contrast rules for each target colour object under different illumination intensities with the presence of similarly coloured objects. The colour calibration algorithm is able to extract colour descriptors in a matter of seconds as compared to manual calibration usually taking hours to complete. Using the robot soccer environment as a test bed, the algorithm is able to calibrate colours with excellent accuracy.