TY - GEN

T1 - Linear algebra operators for GPU implementation of numerical algorithms

AU - Krüger, Jens

AU - Westermann, Rüdiger

PY - 2003

Y1 - 2003

N2 - 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.

AB - 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.

KW - graphics hardware

KW - numerical simulation

UR - http://www.scopus.com/inward/record.url?scp=77954024744&partnerID=8YFLogxK

U2 - 10.1145/1201775.882363

DO - 10.1145/1201775.882363

M3 - Conference contribution

AN - SCOPUS:77954024744

SN - 1581137095

SN - 9781581137095

T3 - ACM SIGGRAPH 2003 Papers, SIGGRAPH '03

SP - 908

EP - 916

BT - ACM SIGGRAPH 2003 Papers, SIGGRAPH '03

T2 - ACM SIGGRAPH 2003 Papers, SIGGRAPH '03

Y2 - 27 July 2003 through 31 July 2003

ER -