The rapid increase in the performance of graphics hardware, coupled with recent improvements in its programmability, have made graphics hardware a compelling platform for computationally demanding tasks in a wide variety of application domains. In this report, we describe, summarize, and analyze the latest research in mapping general-purpose computation to graphics hardware. We begin with the technical motivations that underlie general-purpose computation on graphics processors (GPGPU) and describe the hardware and software developments that have led to the recent interest in this field. We then aim the main body of this report at two separate audiences. First, we describe the techniques used in mapping general-purpose computation to graphics hardware. We believe these techniques will be generally useful for researchers who plan to develop the next generation of GPGPU algorithms and techniques. Second, we survey and categorize the latest developments in general-purpose application development on graphics hardware. This survey should be of particular interest to researchers who are interested in using the latest GPGPU applications in their systems of interest.

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A Survey of General-Purpose Computation on Graphics Hardware

A Survey of General-Purpose Computation on Graphics Hardware.

Many computer graphics applications require high-intensity numerical simulation. We show that such computations can be performed efficiently on the GPU, which we regard as a full function streaming processor with high floating-point performance. We implemented two basic, broadly useful, computational kernels: a sparse matrix conjugate gradient solver and a regular-grid multigrid solver. Real time applications ranging from mesh smoothing and parameterization to fluid solvers and solid mechanics can greatly benefit from these, evidence our example applications of geometric flow and fluid simulation running on NVIDIA's GeForce FX.

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Sparse matrix solvers on the GPU: conjugate gradients and multigrid

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.

https://www.cc.gatech.edu/~jarek/graphics/papers/15GPUsimulationKruger.pdf

Linear algebra operators for GPU implementation of numerical algorithms

The scan primitives are powerful, general-purpose data-parallel primitives that are building blocks for a broad range of applications. We describe GPU implementations of these primitives, specifically an efficient formulation and implementation of segmented scan, on NVIDIA GPUs using the CUDA API. Using the scan primitives, we show novel GPU implementations of quicksort and sparse matrix-vector multiply, and analyze the performance of the scan primitives, several sort algorithms that use the scan primitives, and a graphical shallow-water fluid simulation using the scan framework for a tridiagonal matrix solver.

/pdf/scan-primitives-for-gpu-computing-2y2cnrpzmo.pdf

Scan primitives for GPU computing

In this paper, we present a method for real-time visual simulation of diverse dynamic phenomena using programmable graphics hardware. The simulations we implement use an extension of cellular automata known as the coupled map lattice (CML). CML represents the state of a dynamic system as continuous values on a discrete lattice. In our implementation we store the lattice values in a texture, and use pixel-level programming to implement simple next-state computations on lattice nodes and their neighbors. We apply these computations successively to produce interactive visual simulations of convection, reaction-diffusion, and boiling. We have built an interactive framework for building and experimenting with CML simulations running on graphics hardware, and have integrated them into interactive 3D graphics applications.

Physically-based visual simulation on graphics hardware

We introduce a technique to rapidly generate summed-area tables using graphics hardware. Summed area tables, originally introduced by Crow, provide a way to filter arbitrarily large rectangular regions of an image in a constant amount of time. Our algorithm for generating summed-area tables, similar to a technique used in scientific computing called recursive doubling, allows the generation of a summed-area table in O(log n) time. We also describe a technique to mitigate the precision requirements of summed-area tables. The ability to calculate and use summed-area tables at interactive rates enables numerous interesting rendering effects. We present several possible applications. First, the use of summed-area tables allows real-time rendering of interactive, glossy environmental reflections. Second, we present glossy planar reflections with varying blurriness dependent on a reflected object’s distance to the reflector. Third, we show a technique that uses a summed-area table to render glossy transparent objects. The final application demonstrates an interactive depth-of-field effect using summedarea tables.

/pdf/fast-summed-area-table-generation-and-its-applications-1ompdwmdf9.pdf

Fast Summed-Area Table Generation and its Applications

We present a method that takes a raster image as input and produces a painting-like image composed of strokes rather than pixels. Our method works by first segmenting the image into features, finding the approximate medial axes of these features, and using the medial axes to guide brush stroke creation. System parameters may be interactively manipulated by a user to effect image segmentation, brush stroke characteristics, stroke size, and stroke frequency. This process creates images reminiscent of those contemporary representational painters whose work has an abstract or sketchy quality. Our software is available at http://www.cs.utah.edu/npr/ArtisticVision.

/pdf/artistic-vision-painterly-rendering-using-computer-vision-4a7ypqet99.pdf

Artistic Vision: painterly rendering using computer vision techniques

Radiosity is a widely used technique for global illumination. Typically the computation is performed offline and the result is viewed interactively. We present a technique for computing radiosity, including an adaptive subdivision of the model, using graphics hardware. Since our goal is to run at interactive rates, we exploit the computational power and programmability of modern graphics hardware. Using our system on current hardware, we have been able to compute and display a radiosity solution for a 10,000 element scene in less than one second.

Radiosity on graphics hardware

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Greg Coombe

Papers

Physically-based visual simulation on graphics hardware

Fast Summed-Area Table Generation and its Applications

Artistic Vision: painterly rendering using computer vision techniques

Radiosity on graphics hardware

Physically-based visual simulation on graphics hardware