Multi-threaded parallel tetrahedral mesh improvement by combining atomic operation and graph coloring

In industrial numerical simulations, efficiently generating high-quality tetrahedral meshes remains a significant challenge. Advances in high-performance computing have made parallelization a practical approach to improving the quality of large-scale tetrahedral meshes. This study proposes a fine-grained multithreaded parallel method to accelerate tetrahedral mesh improvement. By utilizing atomic operations, we fundamentally address thread safety concerns. Additionally, through the precise use of atomic operations, task decomposition strategies, and a multithreaded memory model, we minimize the probability of task overlap and data races, thereby enhancing overall parallel mesh improvement efficiency. Experimental results demonstrate that our parallel mesh improver is robust and effective for complex industrial models. On a laptop with 16 threads, we achieved a tenfold increase in tetrahedral mesh improvement speed, with the quality of the improved meshes being comparable to that of the sequential process.