StiffGIPC: Advancing GPU IPC for stiff affine-deformable simulation

TL;DR

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 10× speedup over state-of-the-art GPU IPC methods is proposed.

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.

Figures (24)

• Figure 1: An overview of 1 Newton iteration in our unified GPU IPC framework. Our simulation focuses on cloth, soft bodies with varying stiffness, and stiff affine bodies abd. Cloth and soft bodies are modeled using FEM. Contact between all objects is handled using IPC ipc. We solve the system with a Newton-PCG solver and use Continuous Collision Detection (CCD) to filter the search direction and prevent penetration, applying backtracking line search to ensure energy decrease. Our contributions, highlighted in light pink blocks, include a novel inexact strain limiting energy with an analytic eigensystem for efficient PSD projection, an optimized linear solver with a connectivity-enhanced MAS preconditioner, and a highly-parallelized global Hessian assembly strategy for affine-deformable coupling.
• Figure 2: A node sorting example using Morton code. Red disks represent nodes, green lines show topology connections, and dotted blue lines indicate Morton code order. After sorting, nodes will follow the character sequence shown. Note that this is a contrived example for clarity.
• Figure 3: MAS aggregation of \ref{['fig:mas_morton']} using Morton code. Within each subdomain (size 4 here, separated by dashed blue lines), connected nodes are merged into a super node (orange block) at the next coarser level. The order of the super node is determined by the lowest order of the merged nodes. For example, in level 1, nodes $b$ and $d$ are merged and positioned before $c$ because $b$ has a lower order. The subdomains are then reconstructed from sets of 4 consecutive super nodes, and here this process continues until no further merging is possible at a certain level.
• Figure 4: Our connectivity-enhanced MAS aggregation of \ref{['fig:mas_morton']}. The orange blocks represent super nodes at the coarser levels. At level 0, our method groups nodes based on mesh connectivity, and so each group becomes 1 super node at level 1, completing the aggregation.
• Figure 5: Aligning METIS partitions and MAS subdomains. The red blocks represent subdomains from the METIS partition, the deep blue rectangle shows the MAS subdomain, and the green-blue blocks represent inserted zero entries as padding. (a) An example where the METIS partition sizes are 3 and 4, while the MAS subdomain size is 4, leading to isolated nodes within subdomains and potentially suboptimal aggregation (\ref{['sec:mas_limit']}). (b) Our solution inserts zero entries to prevent isolated nodes caused by misalignment between the METIS partition and MAS subdomains.