This paper presents a novel implicit scheme for the constraint resolution in real-time finite element simulations in the presence of contact and friction. Instead of using the standard motion correction scheme, we propose an iterative method where the constraint forces are corrected in Newton iterations. In this scheme, we are able to update the constraint directions recursively, providing more accurate contact and friction response. However, updating the constraint matrices leads to massive computation costs. To address the issue, we propose separating the constraint direction and geometrical mapping in the contact Jacobian matrix and reformulating the schur-complement of the system matrix. When combined with GPU-based parallelization, the reformulation provides a very efficient updating process for the constraint matrices in the recursive corrective motion scheme. Our method enables the possibility to handle the inconsistency of constraint directions at the beginning and the end of time steps. At the same time, the resolution process is kept as efficient as possible. We evaluate the performance of our fast-updating scheme in a contact simulation and compare it with the standard updating scheme.

翻译：本文提出了一种新颖的隐式方案,用于在存在接触和摩擦的实时有限元仿真中进行约束求解。不同于使用标准的运动校正方案,我们提出了一种迭代方法,在牛顿迭代过程中校正约束力。在该方案中,我们能够递归地更新约束方向,从而提供更精确的接触和摩擦响应。然而,约束矩阵的更新会导致巨大的计算成本。为解决这一问题,我们提出在接触雅可比矩阵中分离约束方向与几何映射,并重新构造系统矩阵的舒尔补。当与基于GPU的并行化相结合时,该重构为递归校正运动方案中的约束矩阵提供了非常高效的更新过程。我们的方法使得处理时间步起始和结束时约束方向不一致性成为可能,同时尽量保持求解过程的高效性。我们在接触仿真中评估了快速更新方案的性能,并将其与标准更新方案进行了对比。