Implementation of a Finite Di erence Method on a Custom Computing Platform

The nite di erence method is a numerical analysis technique used to solve problems involving irregular geometries, complicated boundary conditions, or both. The geometries are represented using partial di erential equations. The solutions to the partial di erential equations can be easily generated with the aid of a computer. As the geometries become increasingly complex, the solutions of the partial di erential equations become computationally more intensive. Con gurable computing machines are an emerging class of computing platform which are characterized by providing the computational performance of application speci c processors, yet retaining the exibility and rapid recon gurability attributed to general-purpose processors over a diversity of tasks. Structural modeling of underwater vehicles relies upon analysis involving complex boundary conditions. The nite di erence method can be used to perform heat and shock analysis on the vehicles. This paper presents an implementation and performance gures for a speci c domain of the nite di erence method { a two-dimensional heat transfer modeling system using a Splash-2 Con gurable Computing Machine (CCM).