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...

Full description

Saved in:
Bibliographic Details
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
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0018-926X
1558-2221
DOI:10.1109/TAP.2025.3541883