SPADIX: A Highly Efficient Accelerator for Solving 3-D Partial Differential Equations

Solving partial differential equations (PDEs) holds immense significance in numerous scientific and engineering fields. While analytical solutions to PDEs are often restricted to simple cases, numerical methods offer powerful techniques to approximate solutions for complex PDEs. Previous works have proposed customized accelerators to address the compute- and memory-intensive aspects of numerical PDE solvers. However, these approaches primarily focus on 2-D PDEs and encounter challenges in scaling to support 3-D PDEs due to increased complexity and computational demands. In this article, we introduce Spadix, a highly efficient hardware accelerator designed for numerical 3-D PDE solvers. Spadix leverages a customized processing element (PE) array architecture specifically tailored to the compute and data access patterns in 3-D PDEs. The PE incorporates techniques such as temporal and spatial data reuse to minimize data accesses, enhancing overall performance and energy efficiency. Additionally, Spadix supports the checkerboard method for numerical PDE solvers, which exhibits a faster convergence rate compared to the Jacobi method without compromising parallelism. Our evaluation demonstrates that Spadix achieves an average $8.4\times $ speedup with $9.2\times $ energy reduction over NVIDIA RTX3090 GPU and a $9.7\times $ speedup with $3.2\times $ energy reduction over Alrescha, the state-of-the-art PDE-solving accelerator.