Reduced order modeling in FDTD with provable stability beyond the CFL limit
Why this work is in the frame
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Bibliographic record
Abstract
The Finite-Difference Time-Domain (FDTD) method is widely used in signal and power integrity, applied electromagnetism, and physics. Unfortunately, its computational efficiency can be severely degraded for multiscale problems, where small and large features coexist. This scenario is common in signal and power integrity, because of the large aspect ratio of interconnects and power/ground planes. In this paper, we show how multiscale FDTD simulations can be accelerated with model order reduction. A detailed model for complex objects is first generated using a fine FDTD grid. The model is then compressed with model order reduction, and embedded into a main coarse grid. During this process, the stability limit of the reduced model can be also extended, enabling the use of a larger time step in the whole domain. Using a passivity argument, we are able to systematically guarantee the stability of the resulting scheme, which is a main novelty with respect to previous works. A numerical example with two reduced models shows the potential of the proposed ideas.
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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 | 0.000 | 0.000 |
| 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 it