A multiscale finite volume method for Maxwell's equations at low frequencies
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Bibliographic record
Abstract
Simulating electromagnetic fields in the quasi-static regime by solving Maxwell's equations is a central task in many geophysical applications. In most cases, geophysical targets of interest exhibit complex topography and bathymetry as well as layers and faults. Capturing these effects with a sufficient level of detail is a huge challenge for numerical simulations. Standard techniques require a very fine discretization that can result in an impracticably large linear system to be solved. A remedy is to use locally refined and adaptive meshes, however, the potential coarsening is limited in the presence of highly heterogeneous and anisotropic conductivities. In this paper, we discuss the application of multiscale finite volume (MSFV) methods to Maxwell's equations in frequency domain. Given a partition of the fine mesh into a coarse mesh the idea is to obtain coarse-to-fine interpolation by solving local versions of Maxwell's equations on each coarsened grid cell. By construction, the interpolation accounts for fine scale conductivity changes, yields a natural homogenization, and reduces the fine mesh problem dramatically in size. To improve the accuracy for singular sources, we use an irregular coarsening strategy. We show that using MSFV methods we can simulate electromagnetic fields with reasonable accuracy in a fraction of the time as compared to state-of-the-art solvers for the fine mesh problem, especially when considering parallel platforms.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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