LAWS: Large-Scale Accelerated Wave Simulations on FPGAs
Dimitrios Gourounas, Bagus Hanindhito, Arash Fathi, Dimitar Trenev, Lizy K. John, Andreas Gerstlauer · 2023
Computing numerical solution to large-scale scientific computing problems described by partial differential equations is a common task in high-performance computing. Improving their performance and efficiency is critical to exa-scale computing. Application-specific hardware design is a well-known solution, but the wide range of kernels makes it infeasible to provision supercomputers with accelerators for all applications. This makes reconfigurable platforms a promising direction. In this work, we focus on wave simulations using discontinuous Galerkin solvers, as an important class of applications. Existing work using FPGAs is limited to accelerating specific kernels or small problems that fit into FPGA BRAM. We present LAWS, a generic and configurable architecture for large-scale accelerated wave simulation problems running on FPGAs out of DRAM. LAWS exploits fine- and coarse-grain parallelism using a scalable array of application-specific cores, and incorporates novel dataflow optimizations, including prefetching, kernel fusion, and memory layout optimizations to minimize data transfers and maximize DRAM bandwidth utilization. We further accompany LAWS with an analytical performance model that allows for scaling across technology trends and architecture configurations. We demonstrate LAWS on the simulation of elastic wave equations. Results show that a single FPGA core achieves 69% higher performance than 24 Xeon cores with 13.27x better energy efficiency, when given 1.94x less peak DRAM bandwidth. Scaling to the same peak DRAM bandwidth shows that an FPGA is 3.27x and 1.5x faster than 24 CPU cores and an Nvidia P100 GPU, with 22.3x and 4.53x better efficiency, respectively.