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...

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Published in:	IEEE transactions on antennas and propagation Vol. 73; no. 4; pp. 2690 - 2695
Main Authors:	Wang, Junjie, Zuo, Sheng, Zhao, Xunwang, Tian, Min, Lin, Zhongchao, Zhang, Yu
Format:	Journal Article
Language:	English
Published:	New York IEEE 01.04.2025 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Accelerators Aggregates Algorithms Antennas and propagation Artificial neural networks Complex structures Data transfer (computers) Electromagnetics Factorization Feature extraction Finite element analysis finite element method (FEM) Format graph convolutional network (GCN) Graph convolutional networks large-scale parallel algorithm Machine learning manycore architecture Parallel processing radiation problems Solvers Sparse matrices Sunway computing systems supernodal factorization algorithm Training Vectors
ISSN:	0018-926X, 1558-2221
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Abstract	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 <inline-formula> <tex-math notation="LaTeX">4.25 \times </tex-math></inline-formula> 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.
AbstractList	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 <inline-formula> <tex-math notation="LaTeX">4.25 \times </tex-math></inline-formula> 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. 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 [Formula Omitted] 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.
Author	Zhao, Xunwang Tian, Min Zuo, Sheng Lin, Zhongchao Zhang, Yu Wang, Junjie
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SubjectTerms	Accelerators Aggregates Algorithms Antennas and propagation Artificial neural networks Complex structures Data transfer (computers) Electromagnetics Factorization Feature extraction Finite element analysis finite element method (FEM) Format graph convolutional network (GCN) Graph convolutional networks large-scale parallel algorithm Machine learning manycore architecture Parallel processing radiation problems Solvers Sparse matrices Sunway computing systems supernodal factorization algorithm Training Vectors
Title	A Parallel Direct Finite Element Solver Empowered by Machine Learning for Solving Large-Scale Electromagnetic Problems
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