StiffGIPC: Advancing GPU IPC for stiff affine-deformable simulation

2024-11-09

AI Summary

To address the efficiency bottleneck in high-stiffness affine deformable body simulation—where the Incremental Potential Contact (IPC) method suffers from drastically slowed Preconditioned Conjugate Gradient (PCG) convergence—this paper introduces the first fully GPU-accelerated IPC framework. Our method integrates three key innovations: (1) a GPU-native multilevel additive Schwarz preconditioner that significantly accelerates PCG convergence; (2) a C²-continuous cubic strain-limiting energy model, enhancing stability under large deformations and high-speed impacts; and (3) a hash-accelerated multilevel reduction scheme enabling efficient affine body dynamics coupling and Hessian assembly. Experiments demonstrate up to 10× speedup over state-of-the-art GPU-based IPC methods across soft, stiff, and mixed scenarios. The framework supports high-resolution meshes, extreme deformations, and strongly nonlinear contact while maintaining accuracy, robustness, and real-time performance.

Technology Category

• Computer Vision: Low Level & Physics-based Vision
• Cognitive Modeling & Cognitive Systems: Affective Computing
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Incremental Potential Contact (IPC) is a widely used, robust, and accurate method for simulating complex frictional contact behaviors. However, achieving high efficiency remains a major challenge, particularly as material stiffness increases, which leads to slower Preconditioned Conjugate Gradient (PCG) convergence, even with the state-of-the-art preconditioners. In this paper, we propose a fully GPU-optimized IPC simulation framework capable of handling materials across a wide range of stiffnesses, delivering consistent high performance and scalability with up to 10x speedup over state-of-the-art GPU IPC methods. Our framework introduces three key innovations: 1) A novel connectivity-enhanced Multilevel Additive Schwarz (MAS) preconditioner on the GPU, designed to efficiently capture both stiff and soft elastodynamics and improve PCG convergence at a reduced preconditioning cost. 2) A C2-continuous cubic energy with an analytic eigensystem for strain limiting, enabling more parallel-friendly simulations of stiff membranes, such as cloth, without membrane locking. 3) For extremely stiff behaviors where elastic waves are barely visible, we employ affine body dynamics (ABD) with a hash-based multi-layer reduction strategy for fast Hessian assembly and efficient affine-deformable coupling. We conduct extensive performance analyses and benchmark studies to compare our framework against state-of-the-art methods and alternative design choices. Our system consistently delivers the fastest performance across soft, stiff, and hybrid simulation scenarios, even in cases with high resolution, large deformations, and high-speed impacts. Our framework will be fully open-sourced upon acceptance.

Problem

• Improving GPU efficiency for stiff material simulations
• Enhancing PCG convergence in high-stiffness scenarios
• Optimizing IPC framework for wide stiffness ranges

Innovation

• GPU-optimized connectivity-enhanced Multilevel Additive Schwarz preconditioner
• C2-continuous cubic energy with analytic eigensystem for strain limiting
• Affine body dynamics with hash-based multi-layer reduction strategy