Barrier-Augmented Lagrangian for GPU-based Elastodynamic Contact

TL;DR

This paper introduces a GPU-accelerated elastodynamic simulation method using a novel barrier-augmented Lagrangian approach, significantly improving efficiency, scalability, and handling of stiff problems in contact modeling.

Contribution

It presents a new barrier-augmented Lagrangian method that enhances system conditioning and solver efficiency for GPU-based elastodynamic contact simulations, enabling large-scale, complex problem solving.

Findings

Achieves significant scalability improvements on GPU hardware.

Handles stiff problems more effectively than existing methods.

Enables simulation of complex collision scenarios with large deformations.

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.