AGIPC: Adaptive In-Solve Algebraic Coarsening for GPU IPC

Xuan Wang, Zhaofeng Luo, Minchen Li, Taku Komura, Kemeng Huang

We present algebraic adaptive in-solve coarsening, a GPU-oriented method that dynamically reduces degrees of freedom (DoF) within the Newton solve of implicit time integration without explicit topological modification. Starting from a fine mesh, adaptivity is expressed as a selective edge-collapse process governed by per-edge tags, defining an implicit coarse mesh whose linear system is assembled algebraically on the GPU.

Key Innovations:

• In-solve adaptive coarsening that requires no remeshing and preserves connectivity and vertex ordering
• Warp-level hash mapping scheme that aggregates collapsible edges in parallel, grouping fine vertices into coarse super-nodes while protected edges preserve local detail
• Algebraic assembly of the coarse system via efficient GPU reduction kernels, solved with preconditioned conjugate gradient (PCG) and prolongated back to the fine mesh
• Seamless integration with IPC’s barrier energy, achieving up to 3x speedup over a state-of-the-art GPU IPC solver with visually indistinguishable results