A Pattern-Aware Finite Element Matrix Assembly Method on GPUs

The Finite Element Method (FEM) is a fundamental technique for solving large-scale and complex engineering problems. During the construction of the system equations, the efficiency of finite element matrix assembly plays a crucial role in the overall performance. However, existing approaches often overlook the sensitivity of assembly algorithm performance to mesh characteristics, making it difficult to achieve optimal performance across diverse problems. In this work, we propose a novel pattern-aware FEM matrix assembly method on GPUs. To this end, we thoroughly analyze the key factors affecting performance and extract a set of potentially influential mesh features and density representations. Based on this, we construct a Deep learning-based prediction model that fully captures the input mesh characteristics to predict the performance-optimal assembly strategy. Experimental results on mesh datasets with a wide range of feature variations demonstrate that our method achieves remarkable prediction accuracy and delivers up to $7.34 \times$ speedup in execution time compared to state-of-the-art approaches. To the best of our knowledge, this is the first work that introduces auto-tuning for the FEM matrix assembly process.