Abstract In this manuscript, we present a novel cutting method that involves using a vertex‐snapping strategy to fit the boundary surface onto the cutting path while avoiding generating new elements. We employ a point cloud with polynomial fitting to generate the cutting path, allowing for operation with unscheduled cuts and potential perturbations. Efficient geometry operations are developed to handle topological changes during progressive cutting. While it is challenging to optimize the mesh quality and accurately align the cut surface with the cutting path, we propose an innovative strategy that converts this geometric problem into a quasi‐static elastic problem. This involves solving a constrained elastic problem within an auxiliary simulation, where the system optimizes the mesh quality when reaching equilibrium. Furthermore, we propose modifications to a GPU‐based matrix‐free solver, enabling efficient updates of the precomputed data stored in the GPU memory and thus ensuring real‐time performance.

We present a GPU-friendly framework for real-time implicit simulation of elastic material in the presence of frictional contacts. The integration of hyperelasticity, non-interpenetration contact, and friction in real-time simulations presents formidable nonlinear and non-smooth problems, which are highly challenging to solve. By incorporating nonlinear complementarity conditions within the local-global framework, we achieve rapid convergence in addressing these challenges. While the structure of local-global methods is not fully GPU-friendly, our proposal of a simple yet efficient solver with sparse presentation of the system inverse enables highly parallel computing while maintaining a fast convergence rate. Moreover, our novel splitting strategy for non-smooth indicators not only amplifies overall performance but also refines the complementarity preconditioner, enhancing the accuracy of frictional behavior modeling. Through extensive experimentation, the robustness of our framework in managing real-time contact scenarios, ranging from large-scale systems and extreme deformations to non-smooth contacts and precise friction interactions, has been validated. Compatible with a wide range of hyperelastic models, our approach maintains efficiency across both low and high stiffness materials. Despite its remarkable efficiency, robustness, and generality, our method is elegantly simple, with its core contributions grounded solely on standard matrix operations.