Accelerated Harmonic-Balance Analysis Using a Graphical Processing Unit Platform
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Bibliographic record
Abstract
This paper describes a new approach to accelerate the simulation of the steady-state response of nonlinear circuits using the harmonic-balance (HB) technique. The approach presented in this paper focuses on the direct factorization of the Jacobian matrix, of the HB nonlinear equations, using a graphical processing unit (GPU) platform. The computational core of the proposed approach is based on developing a block-wise version of the KLU factorization algorithm, where scalar arithmetic operations are replaced by block-aware matrix operations. For a large number of harmonics, or excitation tones, or both, the Block-KLU (BKLU) approach effectively raises the ratio of floating-point operations to other operations and, therefore, becomes an ideal vehicle for implementation on a GPU-based platform. Motivated by this fact, we develop a GPU-based framework to implement the BKLU. The proposed approach yields speedup by up to 89 times over conventional direct factorization on CPU.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 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 it