FROM IIM TO AUGMENTED IIM: A POWERFUL TOOL FOR COMPLEX PROBLEMS USING CARTESIAN MESHES
Bibliographic record
Abstract
The immersed interface method (IIM) ?rst proposed in is an accurate numerical method for solving elliptic interface problems on Cartesian meshes. It is a sharp interface method that was intended to improve accuracy of the immersed boundary (IB) method. The IIM is second order accurate in the maximum norm (pointwise, strongest) while the IB method is ?rst order accurate. The ?rst IIM paper is one of the most downloaded one from the SIAM website and is one of the most cited papers. While IIM provided a way of accurate discretization of the partial differential equations (PDEs) with discontinuous coefficients, the augmented IIM ?rst proposed in made the IIM much more efficient and faster by utilizing existing fast Poisson solvers. More important is that the augmented IIM provides an efficient way for multi-physics models with different governing equations, problems on irregular domains, multi-scales and multi-connected domains. A brie?y introduction of the augmented strategy including some recently progress is presented in this article.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".