GPU-accelerated Finite-Element Method for the Three-dimensional Unstructured Mesh Atmospheric Dynamic Framework

Abstract. The three-dimensional unstructured-mesh finite-element atmospheric dynamical framework is gaining significance owing to its flexibility in representing complex topography and capability for multi-scale simulations in high resolutions. However, this framework has substantial bottlenecks. Unlike structured-grid models, the unstructured finite element method (FEM) must frequently access irregular mesh connectivity among nodes, edges, and elements, causing indirect memory addressing, inadequate data locality, and substantial memory bandwidth bottlenecks on conventional CPU architectures. Consequently, element-wise computations and global assembly are the primary contributors to the runtime in high-resolution simulations.

This study develops a GPU-parallel implementation of the Fluidity-Atmosphere dynamical core to address these challenges. The GPU-oriented data structures and optimized kernels are designed to efficiently leverage the computing power of GPUs. These kernels enable parallelized element integration and are efficient solvers for specific size matrices; a parallel assembly strategy enhances memory throughput during global sparse matrix construction. On the NVIDIA A100 GPU, the optimized kernels achieve speeds over 100× for element-wise computations and up to 389.02 times for global matrix assembly, resulting in an overall acceleration of 8.57 times with four messages passing interface (MPI) processes. The proposed framework demonstrates that tailored GPU parallelization is effective in overcoming the computational bottleneck of unstructured FEM-based atmospheric models, facilitating high-resolution simulations on heterogeneous architectures.