An LUR-Based Fast Frequency Sweep Technique to Expedite the EM Topology Optimization for Waveguide Structures
Bibliographic record
Abstract
Material topology optimization is important in electromagnetics (EMs) optimization. The design space decomposition (DSD) technique has recently been proven efficient in computing the EM response for a single frequency in topology optimization. However, when the considered bandwidth is wide, the increased time of calculating EM responses can be nonnegligible, leading to the consideration of the model order reduction (MOR) technique. This article proposes a novel lower and upper triangular matrix reconstruction (LUR)-based fast frequency sweep (FFS) algorithm, addressing the challenges of combining the MOR into the DSD technique. The proposed LUR-based FFS algorithm includes two new techniques: the proposed LUR formulas and the LUR-based forward/backward (LURFB) substitution algorithm. The LUR formulas are developed based on the small matrices calculated by the DSD, efficiently reconstructing the lower and upper triangular matrices of the new finite element method (FEM) system matrix for the updated topology with minimal computational overhead. The LURFB algorithm is a simplified forward/backward (F/B) substitution algorithm based on the LUR formulas to expedite solving system solutions. Incorporating the above two techniques, the MOR can be embedded into the DSD technique, making the FFS achievable and efficient in EM topology optimization. The proposed method preserves the advantages of the DSD technique and outperforms the DSD technique for owning the FFS. Three waveguide examples are optimized using a genetic algorithm (GA) and evaluated with the proposed method, demonstrating superior time efficiency and friendly memory usage compared to other approaches.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".