A Multigrid Solver for Boundary Value Problems Using Programmable Graphics Hardware
Nolan Goodnight,
Cliff Woolley,
Greg Lewin,
Dave Luebke, and
Greg Humphreys
Eurographics/SIGGRAPH Workshop on Graphics Hardware 2003
Abstract:
We present a case study in the application of graphics hardware to
general-purpose numeric computing. Specifically, we describe a
system, built on programmable graphics hardware, able to solve a
variety of partial differential equations with complex boundary
conditions. Many areas of graphics, simulation, and computational
science require efficient techniques for solving such equations. Our
system implements the multigrid method, a fast and
popular approach to solving large boundary value problems. We
demonstrate the viability of this technique by using it to accelerate
three applications: simulation of heat transfer, modeling of fluid
mechanics, and tone mapping of high dynamic range images. We analyze
the performance of our solver and discuss several issues, including
techniques for improving the computational efficiency of iterative
grid-based computations for the GPU.
Greg Humphreys