Barrier-Augmented Lagrangian for GPU-based Elastodynamic Contact

TL;DR

This work tackles robust, large-scale elastodynamic simulation with frictional contact on GPUs by introducing a barrier-augmented Lagrangian that adaptively updates augmentation sets to improve conditioning. It enables an inexact Newton–PCG solver with a domain-decomposed, stiffness-based warm start and a GPU-friendly sparse storage scheme, eliminating the need for direct factorization. The method integrates efficient GPU collision detection and conservative time-of-impact computation, achieving substantial speedups (up to ~$80\times$) over prior GPU interior-point methods and handling stiff problems that challenged existing approaches. The combination of scalable SpMV storage, adaptive scheduling, and per-iteration friction updates yields robust performance across heterogeneous materials, resolutions, and time steps, enabling simulations previously infeasible on commodity GPUs. This work thus paves the way for real-time or near-real-time, high-fidelity elastodynamic simulations with complex contact on accessible hardware.

Abstract

We propose a GPU-based iterative method for accelerated elastodynamic simulation with the log-barrier-based contact model. While Newton's method is a conventional choice for solving the interior-point system, the presence of ill-conditioned log barriers often necessitates a direct solution at each linearized substep and costs substantial storage and computational overhead. Moreover, constraint sets that vary in each iteration present additional challenges in algorithm convergence. Our method employs a novel barrier-augmented Lagrangian method to improve system conditioning and solver efficiency by adaptively updating an augmentation constraint sets. This enables the utilization of a scalable, inexact Newton-PCG solver with sparse GPU storage, eliminating the need for direct factorization. We further enhance PCG convergence speed with a domain-decomposed warm start strategy based on an eigenvalue spectrum approximated through our in-time assembly. Demonstrating significant scalability improvements, our method makes simulations previously impractical on 128 GB of CPU memory feasible with only 8 GB of GPU memory and orders-of-magnitude faster. Additionally, our method adeptly handles stiff problems, surpassing the capabilities of existing GPU-based interior-point methods. Our results, validated across various complex collision scenarios involving intricate geometries and large deformations, highlight the exceptional performance of our approach.

Figures (29)

• Figure 1: Additive Preconditioner (AP) Alone Does Not Yield Performance Improvements. This is due to the problem's significant nonlinearity caused by varying constraint sets across iterations, which leads to the accurate solutions of the linear subproblems being greatly truncated through line searches. (#cols = 28,378)
• Figure 2: Slack Variables with respect to logarithmic and quadratic penalty, respectively ($\hat{d}=10^{-3}$).
• Figure 3: Twisting Rods. This illustration depicts the rigorous stress testing of four stiff rods ($E=10$ MPa), subjected to high-speed torsion from both ends at an angular velocity of 5/12 r/s for over 18 rounds.
• Figure 4: The Semi-Implicit Friction May Exhibit Noticeable Sticky Artifacts when employing a large step size alongside large friction ($\chi=0.9$) in sharp contacts.
• Figure 5: Dragons & Pachinko. Our fully-implicit friction model accurately captures the dynamics with varying coefficients: (a) $\chi=0.1$ and (b) $\chi=0.3$.