OPTIMIZATION OF DISTRIBUTED-MEMORY PARALLELIZATION OF THE AGGREGATED UNFITTED FINITE ELEMENT METHOD IN AI

The Aggregated Unfitted Finite Element Method (AU-FEM) has emerged as a powerful computational technique in the field of artificial intelligence (AI) for solving complex engineering and scientific problems. However, the AU-FEM's computational cost can be significant, requiring the utilization of distributed-memory parallelization to achieve efficient performance on modern high-performance computing (HPC) systems. In this study, we focus on the optimization of distributed-memory parallelization for the AU-FEM, aiming to enhance its scalability, efficiency, and overall computational performance. we employ a combination of algorithmic enhancements and parallel programming techniques. Firstly, we propose a novel domain decomposition strategy that effectively partitions the computational domain into subdomains, allowing for efficient distribution of work among multiple compute nodes. This approach minimizes inter-node communication and load imbalance, while maximizing the utilization of available computing resources. optimized data structures and parallel algorithms tailored specifically for the AU-FEM, reducing the computational overhead associated with parallelization. We exploit parallelization opportunities at various stages of the AU-FEM pipeline, including mesh generation, assembly of linear systems, and solution of large-scale linear systems. These optimizations leverage modern parallel programming models, such as message passing interface (MPI) and shared-memory parallelism using multi-threading (e.g., OpenMP), to harness the full potential of distributed-memory architectures. we conduct extensive experiments on a range of benchmark problems, varying in size and complexity. Our results demonstrate significant improvements in scalability and computational efficiency compared to existing parallelization approaches. The optimized AU-FEM implementation achieves excellent parallel performance, effectively utilizing the available computing resources to solve large-scale problems within reasonable time frames. Our work contributes to the advancement of the AUFEM as a viable computational tool for AI applications. The proposed optimizations provide valuable insights for researchers and practitioners seeking to harness the power of distributed-memory parallelization to accelerate the AU-FEM and solve complex AI-driven problems more efficientl