Linear algebra operators for GPU implementation of numerical algorithms

By Jens Harald Krüger, Rüdiger Westermann. SIGGRAPH Courses, 2003

696 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Graphics and Computer-Aided Design, Hardware and Architecture

View Paper: https://www.semanticscholar.org/paper/4cbc419a4d0a5b55d3d302d648c0827b5d135f4b

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In Computational Theory and Mathematics

In Computer Graphics and Computer-Aided Design

In Hardware and Architecture

Citations in the corpus

A performance study of general-purpose applications on graphics processors using CUDA (2008, methodology): “A framework for solving linear algebra problems on graphics processors is presented by Krüger et al. [13].”
Model reduction for real-time fluids (2006, methodology): “…have been mapped to the GPU as a stream processor including a Lattice Boltzman Method [Li et al. 2003], Coupled Map Lattice [Harris et al. 2002], semi- Lagrangian solver with boundaries [Wu et al. 2005], and a Poisson solver [Krüger and Westermann 2003; Bolz et al. 2003; Goodnight et al. 2003].”
From CUDA to OpenCL: Towards a performance-portable solution for multi-platform GPU programming (2012, background): “Many research publications thoroughly analyzed the new breed of GPU hardware using languages borrowed from the graphics community [3] [4] [5].”
The OpenGL® Shading Language (2006, background): “On the other hand, they restrict the application of shaders to graphics while some new innovative uses in nongraphics areas like the computation of massively parallelized algorithms were shown [ Kruger03 ].”
To appear in the ACM SIGGRAPH conference proceedings Modular Bases for Fluid Dynamics (positive): “Recent work has mapped a number of Eulerian methods to the GPU, including stable advection [Wu et al. 2005], pressure projection [Krüger and Westermann 2003; Bolz et al. 2003; Goodnight et al. 2003], Lattice Boltzmann methods [Li et al. 2003], and the coupled map lattice [Harris et al. 2002].”
Fast computation of database operations using graphics processors (2004, background): “The high throughput of the fragment processors and direct access to texture memory makes the fragment engines a powerful computation engine for certain numerical algorithms, including dense matrix-matrix multiplication [18], general purpose vector processing [36], visual simulation based on coupled-”
TeraFLOP computing on a desktop PC with GPUs for 3D CFD (2008, neutral): “The use of the GPU to accelerate non-graphics computations has drawn much attention (Bolz et al. 2003, Kru¨ger and Westermann 2003, Buck et al. 2004).”
GPGPU: general purpose computation on graphics hardware (2004, methodology): “For details and examples of more sophisticated solvers, see Bolz et al. 2003, Goodnight et al. 2003, and Krüger and Westermann 2003.”
Brook for GPUs: Stream Computing on Graphics Hardware (2004, methodology): “Applications such as linear algebra [Kr(cid:127)uger and Westermann 2003], physical simulation, [Harris et al. 2003], and a complete ray tracer [Purcell et al. 2002; Carr et al. 2002] have been demonstrated to run on GPUs.”
GPU Cluster for High Performance Computing (2004, background): “Krüger and Westermann [16] and Boltz et al.”
Accelerating Compute-Intensive Applications with GPUs and FPGAs (2008, methodology): “and bioinformatics [9] for FPGAs, and linear algebra [12], database operations [7], K-Means [4], AES encryption [19] and n-body simulations [15] on GPUs.”
Simulation of cloud dynamics on graphics hardware (2003, positive): “Implementation of conjugate gradient on the GPU is feasible ([Bolz, et al. 2003;Krüger and Westermann 2003]), but many passes are required just to compute the large vector inner products required by the algorithm ( O (log 2 N ) passes, where N is the grid resolution).”
Real-time volume graphics (2006, background): “Dynamic volumes arise when performing General-Purpose Computation on Graphics Processor (GPGPU) techniques for simulation, image processing, or segmentation [10, 31, 37, 62, 67, 96, 87, 93].”