Efficient block pivoting for multibody simulations with contact
Bibliographic record
Abstract
Simulating stiff physical systems is a requirement for numerous computer graphics applications, such as VR training for heavy equipment operation. However, iterative linear solvers often perform poorly in such cases, and direct methods involving a factorization of the system matrix are typically preferred for accurate and stable simulations. This can have a detrimental impact on performance, since factorization of the system matrix is costly for complex simulations. In this paper, we present a method for efficiently solving linear systems of stiff physical systems involving contact, where the dynamics are modeled as a mixed linear complementarity problem (MLCP). Our approach is based on a block Bard-type algorithm that applies low-rank downdates to a Cholesky factorization of the system matrix at each pivoting step. Further performance improvements are realized by exploiting low bandwidth characteristics of the factorization. Our method gives up to 3.5x speed-up versus recomputing the factorization based on the index set. Various challenging scenarios are used to demonstrate the advantages of our approach.
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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 | 0.000 | 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".