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.