Higher-order Locally Corrected Nystrom solution of the combined field integral equation based on geometric modelling with NURBS
Bibliographic record
Abstract
Summary form only given. Higher-order (HO) methods for electromagnetic analysis are of high practical interest as they are exponentially more efficient than their low-order counterparts (Jeffrey, et.al., IEEE AP Mag. pp. 294-308, vol. 55, no. 3, June 2013). Such methods also can produce the same accuracy of solution with greatly reduced number of unknowns. The HO Method of Moments (MoM) and HO Locally Corrected Nystrom (LCN) method are two common techniques which yield such benefits. The former, however, is known to require prolonged system matrix fill times compared to that of the LCN method (Notaros, IEEE Trans. Antennas Propag., 56, 2251-2276, 2008). Being an element-based method the HO MoM also renders acceleration techniques such as the multilevel fast multipole algorithm (MLFMA) to be less efficient than the point-based LCN method. For the above reasons MLFMA accelerated HO LCN method is a preferred approach to efficient error-controllable large-scale electromagnetic analysis (Jeffrey, et. al., IEEE AP Mag. pp. 294-308, vol. 55, no. 3, June 2013).In this work we show that the HO convergence to the true solution can be achieved in the LCN solution of CFIE only if a certain degree of geometry smoothness is preserved in the discretized model. Our numerical experiments show that the surface must exhibit continuity to at least first-order spatial derivatives. Surface discretizations leading to the discontinuity in first-order spatial derivatives produce infinite electromagnetic fields at the junctions between the mesh elements. This type of discontinuities is artificially introduced to a smooth surface when bilinear and interpolation curvilinear quadrilaterals are used to discretize the geometry. This calls for the introduction of NonUniform Rational B-Spline (NURBS) surfaces into HO-LCN since continuity of spatial derivatives of NURBS surfaces can be controlled. Furthermore since NURBS surfaces are usually a mixture of arbitrary sized quadrilateral and triangular patches, we demonstrate that one can utilize quadrilateral quadrature rules on triangular patches as a special case of quadrilateral elements when one edge approaches zero.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".