A Preliminary Comparison of MLFMA and $\mathcal{H}$-matrix Acceleration of Locally Corrected Nyström Solutions to Scattering Problems
Bibliographic record
Abstract
Fast solutions of scattering problems with Multi-Level Fast Multipole Method (MLFMM) and <tex>$\mathcal{H}$</tex>-matrix accelerated Locally Corrected Nyström (LCN) discretization of the Electric Field Integral Equation (EFIE), Magnetic Field Integral Equation (MFIE), and Combined Field Integral Equation (CFIE), are discussed and compared in terms of their CPU time usage. Fast iterative solutions of the matrix equations resulting from LCN discretizations of the EFIE and MFIE enabled with MLFMM acceleration of the matrix-vector products have been observed to require heavy preconditioning for realistic targets due to poor conditioning of the pertinent matrices. The application of sufficiently effective near field preconditioning can be comparable in complexity to solving the original matrix equation. <tex>$\mathcal{H}$</tex>-matrix acceleration scheme enables direct solution of the pertinent matrix equation but exhibit a high cost associated with <tex>$\mathcal{H}-\text{LU}$</tex> decomposition. Preliminary comparisons of these two iterative and non-iterative acceleration strategies is provided in this work.
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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 | 0.000 | 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 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".