Linear algebra operators for GPU implementation of numerical algorithms

Jens Krüger, Rüdiger Westermann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

188 Scopus citations


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.

Original languageEnglish
Title of host publicationACM SIGGRAPH 2003 Papers, SIGGRAPH '03
Number of pages9
StatePublished - 2003
EventACM SIGGRAPH 2003 Papers, SIGGRAPH '03 - San Diego, CA, United States
Duration: 27 Jul 200331 Jul 2003

Publication series

NameACM SIGGRAPH 2003 Papers, SIGGRAPH '03


ConferenceACM SIGGRAPH 2003 Papers, SIGGRAPH '03
Country/TerritoryUnited States
CitySan Diego, CA


  • graphics hardware
  • numerical simulation


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