Incremental Potential Contact (IPC) guarantees intersection-free simulation but suffers from high computational costs due to the expensive Hessian assembly and linear solves required by Newton's method. While Preconditioned Nonlinear Conjugate Gradient (PNCG) avoids Hessian assembly, it has historically struggled with poor convergence in stiff, contact-rich scenarios due to the lack of effective preconditioners; simple Jacobi preconditioners fail to capture the global coupling, while advanced hierarchy-based preconditioners like Multilevel Additive Schwarz (MAS) are computationally prohibitive to rebuild at every nonlinear iteration. We present MAS-PNCG, a method that unlocks the power of hierarchical preconditioning for nonlinear optimization. Our key technical innovation is a Sparse-Input Woodbury update algorithm that incrementally adapts the fine-level MAS components to rapidly evolving contact sets. This bypasses the need for full preconditioner rebuilds, reducing maintenance cost to near-zero while capturing the complex spectral properties of the contact system. Furthermore, we replace heuristic PNCG search directions with a Hessian-aware 2D subspace minimization that optimally combines the preconditioned gradient and previous direction. We also apply a fast per-subdomain conservative CCD method that ensures penetration-free trajectories while avoiding overly restrictive global step sizes. Experiments demonstrate that our MAS-PNCG outperforms state-of-the-art Newton-PCG solvers, GIPC and StiffGIPC, both preconditioned with MAS up to 5.66$\times$ and 2.07$\times$ respectively.

翻译：增量势接触（IPC）保证了无相交的模拟，但由于牛顿法所需的高代价Hessian矩阵组装与线性求解，其计算成本高昂。尽管预条件非线性共轭梯度法（PNCG）避免了Hessian矩阵的组装，但在刚性强、接触密集的场景中，因缺乏有效预条件子而长期受困于收敛缓慢：简单的雅可比预条件子无法捕捉全局耦合，而像多重网格叠加施瓦兹（MAS）这类基于层次结构的先进预条件子，若在每个非线性迭代中重建则计算量难以承受。我们提出MAS-PNCG方法，该方法解锁了层次预条件在非线性优化中的潜力。关键技术突破在于一种稀疏输入Woodbury更新算法，能逐步调整精细层级MAS组件以适应快速变化的接触集。这避免了完整预条件子重建的需求，将维护成本降至近乎零，同时捕捉接触系统的复杂谱特性。此外，我们将启发式PNCG搜索方向替换为基于Hessian的二维子空间最小化方法，可最优结合预条件梯度与先前方向。我们还应用了一种快速子域保守CCD方法，在保证无穿透轨迹的同时避免过度保守的全局步长。实验表明，我们的MAS-PNCG方法分别以高达5.66倍和2.07倍的加速比，优于使用MAS预条件的先进牛顿-PCG求解器GIPC和StiffGIPC。