Zhaofeng Luo

Juntian Zheng, Zhaofeng Luo, Minchen Li

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 are open-sourced at https://simulation-intelligence.github.io/barrier-free .

Xuan Wang, Zhaofeng Luo, Minchen Li et al.

Implicit time integration is key to robustly simulating stiff materials and large deformations, but its performance is often dominated by repeatedly solving large linear systems. Adaptive coarsening can reduce this cost by concentrating degrees of freedom (DoF) to where it is most needed, yet conventional explicit remeshing changes connectivity (and often vertex ordering), complicating parallel implementations, harming memory locality, and sometimes being disallowed when it may introduce local geometry intersections. Adaptive subspace approaches avoid topological changes, but basis construction and updates incur irregular data access patterns and typically produce dense system matrices, limiting GPU efficiency and keeping many practical systems CPU-centric. We present algebraic adaptive in-solve coarsening, a GPU-oriented method that dynamically reduces DoF within the Newton solve of implicit time integration without explicit topological modification. Starting from a fine mesh, we express adaptivity as a selective edge-collapse process governed by per-edge tags. Collapsible edges are aggregated in parallel using a warp-level hash mapping scheme that groups fine vertices into coarse super-nodes, while protected edges preserve local detail. This defines an implicit coarse mesh whose linear system is assembled algebraically by mapping and reducing fine-scale gradients and Hessians via efficient GPU reduction kernels. We solve the resulting coarse system with a preconditioned conjugate gradient (PCG) method and then prolongate the solution back to the fine mesh. Our approach integrates seamlessly with IPC's barrier energy and exploits GPU parallelism end-to-end. Across a range of challenging scenarios, we achieve up to 3x speedup over a state-of-the-art GPU IPC solver while producing visually indistinguishable results.

Zhaofeng Luo, Minchen Li, Yupeng Jiang

We propose an overlapping Schwarz space-time refinement framework for the material point method (OS-MPM) to improve computational efficiency in problems with strongly localized deformation, contact, and large geometric nonlinearity. The method decomposes the domain into overlapping coarse and fine subdomains with heterogeneous spatial and temporal resolutions, while retaining standard MPM discretizations within each subdomain. Coarse-fine coupling is achieved through an MPM-specific Schwarz iteration combining mass-weighted spatial transmission and temporal interpolation for sub-cycling. In contrast to refinement strategies based on modified basis functions, transition kernels, or strongly enforced interface constraints, the proposed approach preserves the modular structure of standard MPM and shifts the coupling complexity to nonmatching-grid interface operators within the Schwarz alternating procedure. Numerical examples, including a gravity-driven cantilever beam, Hertzian contact, and an elastic inclusion problem, show that the method reproduces analytical or fine-resolution reference solutions with good accuracy and convergence behavior. In the inclusion benchmark, the proposed framework achieves comparable or slightly lower error than single-domain fine simulations at the finest tested resolutions, while reducing computational cost by up to 9.15 times. A three-dimensional folding example further demonstrates the generality of the framework. These results indicate that the proposed method provides an accurate, modular, and efficient route for local space-time refinement in MPM.