An Iterative FEM Solver for IC Electromagnetic Analysis via Hybrid Geometric-Algebraic Partitioning and Neural Network Optimization

In electromagnetic finite element analysis of integrated circuits (ICs), direct solvers face high time and space complexity in large-scale problems, while traditional iterative methods suffer from unstable, unpredictable convergence and require complex manual configuration. In this article, we propose a practical and efficient iterative solver based on the overlapping additive Schwarz (OAS) preconditioner. We propose a hybrid matrix partitioning algorithm, which combines geometric and algebraic partitioning methods to leverage their complementary strengths. Furthermore, we develop a neural network-based evaluation and optimization system to predict the convergence and computational efficiency of candidate configurations, enabling automated selection of the optimal OAS preconditioner. We test our solver on matrices generated from six diverse IC geometries, including three interconnect structures and three real-world packaging board models. Experimental results show that our solver achieves 100% convergence across all test matrices, while previous OAS-based iterative methods converge for at most 68%. In convergent scenarios, it achieves a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.45\times $</tex-math> </inline-formula> average speedup over the Metis-based OAS iterative solver. Meanwhile, compared to the industry-standard direct solver PARDISO and the commercial FEM solver ANSYS HFSS, it achieves average speedups of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.61\times $</tex-math> </inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.39\times $</tex-math> </inline-formula>, respectively, along with superior parallel scalability.