Linear Algebra Operators for GPU Implementation of Numerical Algorithms
Jens Krüger,Rüdiger Westermann
Computer Graphics and Visualization Group, Technical University Munich, Germany
Background
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.
Associated publications
Slides
Demos & Source
DirectX
- implicit water surface
(to compile the source code you need the DirectX 9.0 April 2005 SDK)
[Win32 bin] [Source]
OpenGL
- implicit water surface
(requires GLEW32, GLUT, OpenGL 2.0 and framebuffer objects)
[Win32 bin] [Source]
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