Variational Elastodynamic Simulation
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3721238.3730726.pdf
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156.23 MB
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Author(s)
Mattos Da Silva, Leticia
Sell?n, Silvia
Pacheco-Tallaj, Natalia
Solomon, Justin
Date Issued
July 27, 2025
Publisher
ACM|Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers
Citation
Leticia Mattos Da Silva, Silvia Sellán, Natalia Pacheco-Tallaj, and Justin Solomon. 2025. Variational Elastodynamic Simulation. In Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Conference Papers (SIGGRAPH Conference Papers '25). Association for Computing Machinery, New York, NY, USA, Article 76, 1–11.
Version
Final published version
Abstract
Numerical schemes for time integration are the cornerstone of dynamical simulations for deformable solids. The most popular time integrators for isotropic distortion energies rely on nonlinear root-finding solvers, most prominently, Newton’s method. These solvers are computationally expensive and sensitive to ill-conditioned Hessians and poor initial guesses; these difficulties can particularly hamper the effectiveness of variational integrators, whose momentum conservation properties require reliable root-finding. To tackle these difficulties, this paper shows how to express variational time integration for a large class of elastic energies as an optimization problem with a “hidden” convex substructure. This hidden convexity suggests uses of optimization techniques with rigorous convergence analysis, guaranteed inversion-free elements, and conservation of physical invariants up to tolerance/numerical precision. In particular, we propose an Alternating Direction Method of Multipliers (ADMM) algorithm combined with a proximal operator step to solve our formulation. Empirically, our integrator improves the performance of elastic simulation tasks, as we demonstrate in a number of examples.
Description
SIGGRAPH Conference Papers ’25, Vancouver, BC, Canada
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1145/3721238.3730726
