A 21×21 Dynamic-Precision Bit-Serial Computing Graph Accelerator for Solving Partial Differential Equations Using Finite Difference Method

Abstract

Partial differential equations (PDEs) are ubiquitous in physics and engineering and used for understanding various physical phenomena, including heat, diffusion, fluid and electrodynamics, and quantum mechanics. Analytical PDE solutions are rare, and hence, we approximate using numerical methods. The finite difference method (FDM) approximates PDEs by computing finite differences between discretized solutions. Since finite differences approximate the derivatives of PDEs, many iterations of high-precision computations are required to achieve higher accuracy in their numerical solutions. Hence, computationally-expensive FDM necessitates the use of high-performance computers. As such, their energy consumption is excessive (e.g. 15mJ per iteration and $\gt 320\mathrm{J}$ in total for solving PDE with $\mathrm{a}128 \times 128$ grid using GPU [1]). Consequently, there is an ever-increasing need for a dedicated hardware accelerator for solving PDEs.