The fast multipole method for the computation of large-scale three-dimensional elastostatics boundary-element problems in underground excavations
Bibliographic record
Abstract
We present the theoretical and computational implementation of an original version of the Fast Multipole Method (FMM) for solving large-scale problems in 3D elastostatics based on the indirect boundary integral fictitious formulation. The conventional boundary element method with N collocation nodes, translates into solving a dense and non-symmetric system of equations, with computational complexity O(N2). Additionally, for large models, storing the system’s matrix in random-access memory (RAM) is intractable, requiring storing sections of the matrix in hard disk. This creates an important burden towards computational cost. The FMM is inspired on the intuitive idea of collecting influences (e.g., gravitational, electromagnetic, acoustic, elastic) from close sources into a single source, using approximations with the flavor of a Taylor expansion. We illustrate the power of the method applied in computing 3D elastostatics models for real-world excavations, running within Rocscience modelling software, where important speed-ups were observed for a wide range of models ranging from 100K up to 1M elements.
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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 | 0.001 | 0.000 |
| 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 | 0.000 |
| 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".