FDMAX: An Elastic Accelerator Architecture for Solving Partial Differential Equations

Partial Differential Equations (PDEs) are widely employed to describe natural phenomena in many science and engineering fields. Many PDEs do not have analytical solutions, hence, numerical methods have become prevalent for approximating PDE solutions. The most widely used numerical method is the Finite Difference Method (FDM), which requires fine grids and high-precision numerical iterations that are both compute- and memory-intensive. PDE-solving accelerators have been proposed in the literature, however, they usually focus on specific types of PDEs with rigid grid sizes which limits their broader applicability. Besides, they rarely provided insight into the optimizations of parallel computing and data accesses for solving PDEs, which hinders further improvements in performance and energy efficiency. This paper presents FDMAX, an elastic accelerator to efficiently support FDM for different types of PDEs with any grid size. FDMAX employs a customized Processing Element (PE) array architecture that maximizes data reuse with minimized interconnection overhead. The PE array can be reconfigured to break into a set of subarrays to adapt to different grid sizes for optimal efficiency. Moreover, the PE array exploits computation and data reuse for increased performance and energy efficiency, and is reconfigurable to support a wide range of PDEs such as elliptic, parabolic, and hyperbolic equations. Evaluated on four well-known PDEs, our simulation results show that FDMAX achieves on average 1189× speedup with 1123× energy reduction over Intel Xeon CPU, and 4.9× speedup with 6.3× energy reduction over NVIDIA RTX3090 GPU, and 2.9× speedup over Alrescha, the state-of-the-art PDE-solving accelerator.