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 will be open-sourced.
Fig. 1. Squishy balls under extreme compression. Five elastic squishy balls are compressed by a moving boundary to extreme stress, generating dense contacts, and then released to rebound. The scene contains 2.61M DoFs, 2.25M tetrahedra, and generates up to 1.45M active contact constraints. With significantly fewer Newton iterations and better conditioning, we achieve a 98.5× speedup over GIPC [Huang et al. 2024], averaging 5.37 s per frame.
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 firstorder 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 103× speedup over GIPC on challenging, contact-rich benchmarks -scenarios that were previously tractable only with barrier-based methods. Our code and data will be open-sourced.
CCS Concepts: • Computing methodologies → Physical simulation.
Additional Key Words and Phrases: Finite Element Method, Elastodynamics, Collision Handling, Constrained Optimization, Active Set Method
In recent years, Incremental Potential Contact (IPC) [Li et al. 2020a] has pioneered the penetration-free simulation of nonlinear elastic solids, offering guaranteed algorithmic convergence, solution accuracy, and minimal tuning of algorithmic parameters. IPC has been successfully applied to simulate a range of challenging phenomena. However, its computational efficiency remains a key bottleneck in time-sensitive applications such as robotics and virtual reality, even with recent GPU-accelerated variants featuring highly optimized Gauss-Newton and preconditioned conjugate gradient (PCG) solvers [Huang et al. 2024[Huang et al. , 2025a]].
We identify two major sources of inefficiency in IPC: (1) the use of logarithmic barrier functions leads to severely ill-conditioned systems, requiring many PCG iterations to solve; and (2) IPC suffers from the TOI locking issue [Lan et al. 2023] in collision-intensive scenarios, where its filtered line search severely slows down active set exploration, a process that is inherently combinatorially complex in inequality-constrained optimization.
The TOI locking problem arises because each Newton update is truncated by the smallest time-of-impact (TOI) detected via continuous collision detection (CCD) [Li et al. 2021;Wang et al. 2021], causing the earliest contact to stall the entire optimization step (Figure 2). As a result, many iterations are needed to progressively discover and incorporate all relevant contact pairs into the constraint set. Recent Gauss-Seidel-type strategies [Chen et al. 2025;Lan et al. 2023] attempt to mitigate this issue using local updates, but remain limited in scenarios involving high stiffness or large deformations, due to their reliance on sublinearly convergent coordinate descent methods.
In this work, we propose a novel alternative that retains superlinearly convergent Newton iterations while improving active set exploration efficiency. Our method immediately incorporates all requisite contacts detected by CCD into subsequent iterations, allowing earlier response to all these potential contacts. The key insight stems from reexamining IPC’s CCD-truncated Newton updates as shown in Figure 2: in each iteration, a possibly penetrating state x is generated from the previous penetration-free iterate x last , after which IPC applies CCD to obtain a new penetration-free state x by truncating the path between x last and x. IPC then discards x and proceeds from x, potentially losing information of all contact pairs with larger TOI at x. Instead, we resume Newton iterations directly from x, allowing contacts with larger TOI to generate immediate r
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