Exploration of FPGA-Based Hardware Designs for QR Decomposition for Solving Stiff ODE Numerical Methods Using the HARP Hybrid Architecture

Abstract

In this article, we focus on the acceleration of a chemical reaction simulation that relies on a system of stiff ordinary differential equation (ODEs) targeting heterogeneous computing systems with CPUs and field-programmable gate arrays (FPGAs). Specifically, we target an essential kernel of the coupled chemistry aerosol-tracer transport model to the Brazilian developments on the regional atmospheric modeling system (CCATT-BRAMS). We focus on a linear solve step using the QR factorization based on the modified Gram-Schmidt method as the basis of the ODE solver in this application. We target Intel hardware accelerator research program (HARP) architecture with the OpenCL programming environment for these early experiments. Our design exploration reveals a hardware design that is up to 4 times faster than the original iterative Jacobi method used in this solver. Still, even with hardware support, the overall performance of our QR-based hardware is lower than its original software version.