Abstract: We present a novel multi-layer method for extended position-based dynamics that exploits a sequence of reduced models consisting of rigid and elastic parts to speed up convergence. Taking inspiration from concepts like adaptive rigidification and long-range constraints, we automatically generate different rigid bodies at each layer based on the current strain rate. During the solve, the rigid bodies provide coupling between progressively less distant vertices during layer iterations, and therefore the fully elastic iterations at the final layer start from a lower residual error. Our layered approach likewise helps with the treatment of contact, where the mixed solves of both rigid and elastic in the layers permit fast propagation of impacts. We show several experiments that guide the selection of parameters of the solver, including the number of layers, the iterations per layers, as well as the choice of rigid patterns. Overall, our results show lower compute times for achieving a desired residual reduction across a variety of simulation models and scenarios.
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Authors
Alexandre Mercier-Aubin, and Paul G. Kry
Embedded paper
Context
What if we could eliminate the need for an oracle in adaptive rigidification? This paper presents our answer to that question. We explored the idea of employing a multigrid-inspired approach to solve for motions accurately, thus removing the necessity to predict deformation in reduced chunks. Initially, we experimented with V-Cycle methods, but the results were not ideal. We found that starting with rigid components and gradually introducing elasticity proved to be highly effective. Because of this, our solver deviates from traditional multigrid methods, as the prolongation (or refinement) operator is seldom used.
Github link
click here for the code if you missed the two github buttons
Bibtex
@article{MLXPBD,
journal = {Computer Graphics Forum},
title = {A Multi-layer Solver for XPBD},
author = {Mercier-Aubin, Alexandre and Kry, Paul G.},
year = {2024},
volume = {43},
number = {8},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
doi = {10.1111/cgf.15186},
keywords = {XPBD, rigid bodies, soft bodies, multigrid, contact}
}