Robust and Efficient Penetration-Free Elastodynamics without Barriers

We introduce a barrier-free optimization framework for non-penetration elastodynamic simulation that matches the robustness of Incremental Potential Contact (IPC) while overcoming its two primary efficiency bottlenecks: (1) reliance on logarithmic barrier functions to enforce non-penetration constraints, which leads to ill-conditioned systems and significantly slows down the convergence of iterative linear solvers; and (2) the time-of-impact (TOI) locking issue, which restricts active-set exploration in collision-intensive scenes and requires a large number of Newton iterations. We propose a novel second-order constrained optimization framework featuring a custom augmented Lagrangian solver that avoids TOI locking by immediately incorporating all requisite contact pairs detected via CCD, enabling more efficient active-set exploration and leading to significantly fewer Newton iterations. By adaptively updating Lagrange multipliers rather than increasing penalty stiffness, our method prevents stagnation at zero TOI while maintaining a well-conditioned system. We further introduce a constraint filtering and decay mechanism to keep the active set compact and stable. A comprehensive set of experiments demonstrates the efficiency, robustness, finite-step termination, and first-order time integration accuracy of our method under a cumulative TOI-based termination criterion. With a GPU-optimized simulator design, our method achieves an up to 103× speedup over GIPC on challenging, contact-rich benchmarks – scenarios that were previously tractable only with barrier-based methods. Our code and data are open-sourced at https://simulation-intelligence.github.io/barrier-free.