Speedup using Flowpaths for a Finite Difference Solution of a 3D Parabolic PDE

Abstract

Partial differential equations (PDEs) are used to model physical phenomena and then appropriate convergent numerical algorithms are employed to solve them and create computer simulations.In many important applications, such as weather prediction and contaminant transport processes, simulation outputs are required in real time or even faster, yet the spatial component of the problem is very large, thereby increasing the computational time. In addition, often times numerical scientists work in groups to create a large-scale code, but they work individually on PCs to test components of the code, so that speedup of the computational algorithms on PCs is desirable. There is a benefit to creating and using custom hardware to perform the numerical calculations faster than commodity hardware.This work uses a high-level programming language (Java) to behaviorally describe, and then implement, a finite difference solution of a parabolic PDE as a custom hardware circuit targeted to an FPGA. The results show that the circuits can perform the calculations 1 to 2 orders of magnitude faster than commodity hardware.