Barrier-Augmented Lagrangian for GPU-based Elastodynamic Contact
arxiv(2024)
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.
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