In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism and efficient communication on modern GPUs. Besides performance gains due to improved numerical computations, graphics algorithms benefit from this model in that the transfer of computation results to the graphics processor for display is avoided. We demonstrate the effectiveness of our approach by implementing direct solvers for sparse matrices, and by applying these solvers to multi-dimensional finite difference equations, i.e. the 2D wave equation and the incompressible Navier-Stokes equations.

Abstract—A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs. Index Terms—Image segmentation, interactive segmentation, graph theory, random walks, combinatorial Dirichlet problem, harmonic functions, Laplace equation, graph cuts, boundary completion. Ç 1

In this paper, we present Brook for GPUs, a system for general-purpose computation on programmable graphics hardware. Brook extends C to include simple data-parallel constructs, enabling the use of the GPU as a streaming coprocessor. We present a compiler and runtime system that abstracts and virtualizes many aspects of graphics hardware. In addition, we present an analysis of the effectiveness of the GPU as a compute engine compared to the CPU, to determine when the GPU can outperform the CPU for a particular algorithm. We evaluate our system with five applications, the SAXPY and SGEMV BLAS operators, image segmentation, FFT, and ray tracing. For these applications, we demonstrate that our Brook implementations perform comparably to hand-written GPU code and up to seven times faster than their CPU counterparts.

We present a modified photon mapping algorithm capable of running entirely on GPUs. Our implementation uses breadth-first photon tracing to distribute photons using the GPU. The photons are stored in a grid-based photon map that is constructed directly on the graphics hardware using one of two methods: the first method is a multipass technique that uses fragment programs to directly sort the photons into a compact grid. The second method uses a single rendering pass combining a vertex program and the stencil buffer to route photons to their respective grid cells, producing an approximate photon map. We also present an efficient method for locating the nearest photons in the grid, which makes it possible to compute an estimate of the radiance at any surface location in the scene. Finally, we describe a breadth-first stochastic ray tracer that uses the photon map to simulate full global illumination directly on the graphics hardware. Our implementation demonstrates that current graphics hardware is capable of fully simulating global illumination with progressive, interactive feedback to the user.

We present new algorithms for performing fast computation of several common database operations on commodity graphics processors. Specifically, we consider operations such as conjunctive selections, aggregations, and semi-linear queries, which are essential computational components of typical database, data warehousing, and data mining applications. While graphics processing units (GPUs) have been designed for fast display of geometric primitives, we utilize the inherent pipelining and parallelism, single instruction and multiple data (SIMD) capabilities, and vector processing functionality of GPUs, for evaluating boolean predicate combinations and semi-linear queries on attributes and executing database operations efficiently. Our algorithms take into account some of the limitations of the programming model of current GPUs and perform no data rearrangements. Our algorithms have been implemented on a programmable GPU (e.g. NVIDIA’s GeForce FX 5900) and applied to databases consisting of up to a million records. We have compared their performance with an optimized implementation of CPU-based algorithms. Our experiments indicate that the graphics processor available on commodity computer systems is an effective co-processor for performing database operations.

Utilizing graphics hardware for general purpose numerical computations has become a topic of considerable interest. The implementation of streaming algorithms, typified by highly parallel computations with little reuse of input data, has been widely explored on GPUs. We relax the streaming model's constraint on input reuse and perform an in-depth analysis of dense matrix-matrix multiplication, which reuses each element of input matrices O(n) times. Its regular data access pattern and highly parallel computational requirements suggest matrix-matrix multiplication as an obvious candidate for efficient evaluation on GPUs but, surprisingly we find even nearoptimal GPU implementations are pronouncedly less efficient than current cache-aware CPU approaches. We find the key cause of this inefficiency is that the GPU can fetch less data and yet execute more arithmetic operations per clock than the CPU when both are operating out of their closest caches. The lack of high bandwidth access to cached data will impair the performance of GPU implementations of any computation featuring significant input reuse.

Inspired by the attractive Flops/dollar ratio and the incredible growth in the speed of modern graphics processing units (GPUs), we propose to use a cluster of GPUs for high performance scientific computing. As an example application, we have developed a parallel flow simulation using the lattice Boltzmann model (LBM) on a GPU cluster and have simulated the dispersion of airborne contaminants in the Times Square area of New York City. Using 30 GPU nodes, our simulation can compute a 480x400x80 LBM in 0.31 second/step, a speed which is 4.6 times faster than that of our CPU cluster implementation. Besides the LBM, we also discuss other potential applications of the GPU cluster, such as cellular automata, PDE solvers, and FEM.

We present a novel algorithm to solve dense linear systems using graphics processors (GPUs). We reduce matrix decomposition and row operations to a series of rasterization problems on the GPU. These include new techniques for streaming index pairs, swapping rows and columns and parallelizing the computation to utilize multiple vertex and fragment processors. We also use appropriate data representations to match the rasterization order and cache technology of graphics processors. We have implemented our algorithm on different GPUs and compared the performance with optimized CPU implementations. In particular, our implementation on a NVIDIA GeForce 7800 GPU outperforms a CPU-based ATLAS implementation. Moreover, our results show that our algorithm is cache and bandwidth efficient and scales well with the number of fragment processors within the GPU and the core GPU clock rate. We use our algorithm for fluid flow simulation and demonstrate that the commodity GPU is a useful co-processor for many scientific applications. 1

Deformable isosurfaces, implemented with level-set methods, have demonstrated a great potential in visualization for applications such as segmentation, surface processing, and surface reconstruction. Their usefulness has been limited, however, by two problems. First, 3D level sets are relatively slow to compute. Second, their formulation usually entails several free parameters that can be dicult to tune correctly for speci c applications. The second problem is compounded by the rst. This paper presents a solution to these challenges by describing graphics processor (GPU) based algorithms for solving and visualizing level-set solutions at interactive rates. Our ecient GPUbased solution relies on packing the level-set isosurface data into a dynamic, sparse texture format. As the level set moves, this sparse data structure is updated via a novel GPU to CPU message passing scheme. When the level-set solver is integrated with a real-time volume renderer operating on the same packed format, a user can visualize and steer the deformable level-set surface as it evolves. In addition, the resulting isosurface can serve as a region-of-interest speci er for the volume renderer. This paper demonstrates the capabilities of this technology for interactive volume visualization and segmentation.

We present a memory model to analyze and improve the performance of scientific algorithms on graphics processing units (GPUs). Our memory model is based on texturing hardware, which uses a 2D block-based array representation to perform the underlying computations. We incorporate many characteristics of GPU architectures including smaller cache sizes, 2D block representations, and use the 3C’s model to analyze the cache misses. Moreover, we present techniques to improve the performance of nested loops on GPUs. In order to demonstrate the effectiveness of our model, we highlight its performance on three memory-intensive scientific applications – sorting, fast Fourier transform and dense matrix-multiplication. In practice, our cache-efficient algorithms for these applications are able to achieve memory throughput of 30–50 GB/s on a NVIDIA 7900 GTX GPU. We also compare our results with prior GPU-based and CPU-based implementations on highend processors. In practice, we are able to achieve 2–5× performance improvement.