Energy-Controllable Time Integration for Elastodynamic Contact
🤖 AI Summary
Traditional numerical integrators struggle to simultaneously ensure energy controllability, numerical stability, and physical fidelity in elastodynamic simulations, often failing under large time steps or complex contact scenarios. This work proposes the A-search integrator—a novel variant of implicit Euler grounded in symplectic structure and augmented with a barrier-based energy model—that for the first time unifies stable, penetration-free simulation with tunable energy dissipation or conservation. The method preserves symplecticity in linear systems and demonstrates robustness in nonlinear large-deformation and collision-rich settings. Experimental results show that, at comparable computational cost, A-search outperforms conventional schemes such as BDF2 by effectively preserving low-frequency motion energy and producing visually superior, physically more plausible simulations.
Application Category
📝 Abstract
Dynamic simulation of elastic bodies is a longstanding task in engineering and computer graphics. In graphics, numerical integrators like implicit Euler and BDF2 are preferred due to their stability at large time steps, but they tend to dissipate energy uncontrollably. In contrast, symplectic methods like implicit midpoint can conserve energy but are not unconditionally stable and fail on moderately stiff problems. To address these limitations, we propose a general class of numerical integrators for Hamiltonian problems which are symplectic on linear problems, yet have superior stability on nonlinear problems. With this, we derive a novel energy-controllable time integrator, A-search, a simple modification of implicit Euler that can follow user-specified energy targets, enabling flexible control over energy dissipation or conservation while maintaining stability and physical fidelity. Our method integrates seamlessly with barrier-type energies and allows for inversion-free and penetration-free guarantees, making it well-suited for handling large deformations and complex collisions. Extensive evaluations over a wide range of material parameters and scenes demonstrate that A-search has biases to keep energy in low frequency motion rather than dissipation, and A-search outperforms traditional methods such as BDF2 at similar total running times by maintaining energy and leading to more visually desirable simulations.
Problem
Research questions and friction points this paper is trying to address.
elastodynamic simulation
energy control
numerical integration
contact handling
Hamiltonian systems
Innovation
Methods, ideas, or system contributions that make the work stand out.
energy-controllable integration
symplectic integrator
A-search
elastodynamic contact
implicit Euler modification
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