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, along with a theoretical justification of our method's finite-step termination and first-order time integration accuracy under a cumulative TOI-based termination criterion. A comprehensive set of experiments demonstrates the efficiency, robustness, and accuracy of our method. With a GPU-optimized simulator design, our method achieves an up to 103x speedup over GIPC on challenging, contact-rich benchmarks - scenarios that were previously tractable only with barrier-based methods. Our code and data will be open-sourced.

翻译：我们提出了一种无屏障优化框架，用于非穿透弹性动力学模拟，该框架在保持增量势能接触法鲁棒性的同时，克服了其两个主要的效率瓶颈：(1) 依赖对数屏障函数来强制执行非穿透约束，这会导致系统病态并显著减慢迭代线性求解器的收敛速度；(2) 碰撞时间锁定问题，该问题限制了碰撞密集型场景中的有效集探索，并需要大量的牛顿迭代。我们提出了一种新颖的二阶约束优化框架，其特点是采用定制的增广拉格朗日求解器，通过立即纳入通过连续碰撞检测发现的所有必要接触对来避免TOI锁定，从而实现更高效的有效集探索并显著减少牛顿迭代次数。通过自适应更新拉格朗日乘子而非增加惩罚刚度，我们的方法防止了零TOI处的停滞，同时保持了系统的良态性。我们进一步引入了约束过滤与衰减机制，以保持有效集的紧凑与稳定，并从理论上证明了我们的方法在基于累积TOI的终止准则下具有有限步终止性和一阶时间积分精度。一系列综合实验证明了我们方法的效率、鲁棒性和准确性。通过GPU优化的模拟器设计，我们的方法在具有挑战性、接触密集的基准测试上相比GIPC实现了高达103倍的加速——这些场景以前只有基于屏障的方法才能处理。我们的代码和数据将开源。