Schur Complement-based Substructuring of Stiff Multibody Systems with Contact
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Bibliographic record
Abstract
Substructuring permits parallelization of physics simulation on multi-core CPUs. We present a new substructuring approach for solving stiff multibody systems containing both bilateral and unilateral constraints. Our approach is based on non-overlapping domain decomposition with the Schur complement method, which we extend to systems involving contact formulated as a mixed bounds linear complementarity problem. At each time step, we alternate between solving the subsystem and interface constraint impulses, which leads to the identification of the active constraints. By using the active constraints to compute the effective mass of subsystems within the interface solve, we obtain an exact solution. We demonstrate that our simulations have preferable behavior compared to standard iterative solvers and substructuring techniques based on the exchange of forces at interface bodies. We observe considerable speedups for structured simulations where a user-defined partitioning can be applied, and moderate speedups for unstructured simulations, such as piles of bodies. In the latter case, we propose an automatic partitioning strategy based on the degree of bodies in the constraint graph. Because our method makes use of direct solvers, we are able to achieve interactive and real-time frame rates for a number of challenging scenarios involving large mass ratios, redundant constraints, and ill-conditioned systems.
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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 | 0.000 |
| 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 it