A Multigrid Solver for Boundary-Value Problems Using Programmable Graphics Hardware

Abstract

We present a method for using programmable graphics hardware to solve a variety of boundary value problems. The time-evolution of such problems is frequently governed by partial differential equations, which are used to describe a wide range of dynamic phenomena including heat transfer and fluid mechanics. The need to solve these equations efficiently arises in many areas of computational science. Finite difference methods are commonly used for solving partial differential equations; we show that this approach can be mapped onto a modern graphics processor. We demonstrate an implementation of the multigrid method, a fast and popular approach to solving boundary value problems, on two modern graphics architectures. Our initial tests with available hardware show speedups of roughly 15x compared to traditional software implementation. This work presents a novel use of computer hardware and raises the intriguing possibility that we can make the inexpensive power of modern commodity graphics hardware accessible to and useful for the simulation community. Note: Abstract extracted from PDF text