Periodic Anderson Acceleration for GPU-based Elastic Body Simulation 61

Vertex Block Descent (VBD) solves implicit time integration through parallel per-vertex Newton steps, offering unconditional stability and GPU efficiency for elastic body simulation. Because its block Gauss-Seidel update propagates information only locally, low-frequency error modes spanning the mesh decay slowly across iterations. Chebyshev acceleration improves asymptotic convergence, but does not directly eliminate the globally correlated residuals. We introduce periodic Anderson Acceleration (PAA) for VBD, where a small least-squares mixing step is applied every K iterations between Chebyshev-accelerated sweeps. The two accelerators are complementary: Chebyshev drives fast local convergence while Anderson Acceleration (AA) corrects global error modes through cross-vertex coupling extracted from recent iterates. A fused GPU kernel computes the full Gram system in a single pass, limiting overhead to under 5%. We show that periodic application with a window of m=2 outperforms every-iteration AA, as Chebyshev-accelerated iterates sampled at intervals provide a more linearly independent mixing basis. Combined with per-tet stiffness ramping, PAA reduces the final elastic energy by 6-49% over Chebyshev-only VBD at less than 5% wall-clock overhead, with the largest gains on geometrically complex meshes and extreme deformations. PAA requires no global matrix assembly, no mesh hierarchy, and adds a single integer parameter.