An Iterative FEM Solver for IC Electromagnetic Analysis via Hybrid Geometric-Algebraic Partitioning and Neural Network Optimization
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".