A Multigrid Solver for Boundary Value Problems Using Programmable Graphics Hardware

Abstract

We present a case study in the application of graphics hardware to general-purpose numeric computing. Specifi- cally, 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.