A Parallel Direct Finite Element Solver Empowered by Machine Learning for Solving Large-Scale Electromagnetic Problems

In this communication, a parallel direct finite element solver is proposed for solving complex electromagnetic problems. Our proposed solver features adaptive fill-reducing ordering and highly assembled lazy offloading (HALO) factorization. In our adaptive fill-reducing ordering approach, we propose a graph convolutional network (GCN) model that adaptively selects the optimal fill-reducing ordering method for each electromagnetic problem. Furthermore, we propose a graph sampling training algorithm to enhance the scalability of the GCN model. In our HALO factorization approach, we focus on small irregular level-1 BLAS (BLAS-1) and level-2 BLAS (BLAS-2) subproblems for the supernode factorization and panel update steps, aggregate unstructured L and U factors stored in vector format into structured dense blocks stored in matrix format, assemble these small irregular BLAS-1 and BLAS-2 subproblems into highly assembled level-3 BLAS (BLAS-3) problems that are well-suited for the parallelism of various dedicated manycore accelerators, and propose a lazy offloading technique to achieve high computational efficiency and low data transfer overhead. Our numerical results demonstrate that our proposed method exhibits high accuracy and significant performance improvement for a variety of complex electromagnetic problems and arbitrarily shaped radiating and coupling objects. Moreover, our proposed solver can achieve a $4.25 \times $ speedup in comparison to the state-of-the-art swSuperLU on Sunway manycore computing systems, which is an unprecedented performance gain for the direct finite element solver on dedicated manycore accelerators.