Data and source code for "Semi matrix-free twogrid preconditioners for the Helmholtz equation with near optimal shifts"
Bibliographic record
Abstract
This archive contains the data and source code accompanying the article "Semi matrix-free twogrid preconditioners for the Helmholtz equation with near optimal shifts" The Helmholtz multigrid implementation is based on the MFEM version with git commit id 5457d033d457db5b3543fa47e97b69566baad21e Please use this commit id for a diff in order to see all the modifications and additions provided by this archive. The main Helmholtz multigrid implementation used in the article is located in "examples/helmholtz_mg" with two target executables: - "helmholtz_mg_generate.cpp" contains the code which generates the training data used for the subsequent nonlinear regression - "helmholtz_mg.cpp" computes the solution for a specified scenario and complex shift strategy Moreover, we include the snippets used to postprocess the generated training data in "examples/helmholtz_mg/snippets". The subdirectories are: - "postprocess" contains the generated training data used in the article and a postprocess script for further processing - "approximate" contains the script to perform the nonlinear regression on the previously postprocessed data Installation notes: MFEM must be compiled with MPI and the following additional packages must be enabled: - Hypre - Metis - PETSc with MUMPS The implementation was tested with the following versions: - openmpi-4.0.5 - hypre-2.20.0 - metis-5.1.0 - petsc-3.14.1 - mumps-5.3.3 The Python snippets additionally depend on: - NumPy - SymPy, - PyTorch - Matplotlib - Pandas
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.005 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.005 | 0.003 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.466 | 0.361 |
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".