This GH2003 paper by Goodnight et al. at the University of Virginia is a demonstrates an implementation on of the multigrid method for solving boundary value problems, such as the systems of partial differential equations that arise in physical simulation problems like fluid flow, heat transfer, and tone mapping. This paper is an expanded, more detailed version of the authors’ earlier tech report. (A Multigrid Solver for Boundary Value Problems Using Programmable Graphics Hardware. Nolan Goodnight, Cliff Woolley, Gregory Lewin, David Luebke, and Greg Humphreys. To appear in the proceedings of Graphics Hardware 2003.)