Incremental Potential Contact (IPC) is a widely used, robust, and accurate method for simulating complex frictional contact behaviors. However, achieving high efficiency remains a major challenge, particularly as material stiffness increases, which leads to slower Preconditioned Conjugate Gradient (PCG) convergence, even with the state-of-the-art preconditioners. In this paper, we propose a fully GPU-optimized IPC simulation framework capable of handling materials across a wide range of stiffnesses, delivering consistent high performance and scalability with up to 10x speedup over state-of-the-art GPU IPC methods. Our framework introduces three key innovations: 1) A novel connectivity-enhanced Multilevel Additive Schwarz (MAS) preconditioner on the GPU, designed to efficiently capture both stiff and soft elastodynamics and improve PCG convergence at a reduced preconditioning cost. 2) A C2-continuous cubic energy with an analytic eigensystem for strain limiting, enabling more parallel-friendly simulations of stiff membranes, such as cloth, without membrane locking. 3) For extremely stiff behaviors where elastic waves are barely visible, we employ affine body dynamics (ABD) with a hash-based multi-layer reduction strategy for fast Hessian assembly and efficient affine-deformable coupling. We conduct extensive performance analyses and benchmark studies to compare our framework against state-of-the-art methods and alternative design choices. Our system consistently delivers the fastest performance across soft, stiff, and hybrid simulation scenarios, even in cases with high resolution, large deformations, and high-speed impacts. Our framework will be fully open-sourced upon acceptance.

翻译：增量势能接触法是一种广泛使用、鲁棒且精确的模拟复杂摩擦接触行为的方法。然而，实现高效率仍然是一个重大挑战，尤其是在材料刚度增加时，即使采用最先进的预处理器，也会导致预处理共轭梯度法的收敛速度变慢。本文提出了一种完全GPU优化的IPC仿真框架，能够处理广泛刚度范围内的材料，提供一致的高性能和可扩展性，相比最先进的GPU IPC方法实现高达10倍的加速。我们的框架引入了三项关键创新：1）一种在GPU上实现的新型连通性增强多级加法施瓦茨预处理器，旨在高效捕捉刚性和软性弹性动力学，并以更低的预处理成本改善PCG收敛性。2）一种具有解析特征系统的C2连续三次能量用于应变限制，使得刚性膜（如布料）的模拟更易于并行化，且无膜锁定现象。3）针对弹性波几乎不可见的极端刚性行为，我们采用基于哈希的多层降阶策略的仿射体动力学，以实现快速Hessian矩阵组装和高效的仿射-可变形耦合。我们进行了广泛的性能分析和基准研究，将我们的框架与最先进的方法及其他设计方案进行比较。即使在具有高分辨率、大变形和高速碰撞的场景中，我们的系统在软性、刚性和混合仿真场景下均能持续提供最快的性能。我们的框架将在论文被接受后完全开源。