STA-FEM: Exact Streaming Assembly for Preplanned Dynamic Tetrahedral Topology Edits

TL;DR

STA-FEM introduces a streaming assembly method for dynamic tetrahedral meshes that significantly speeds up simulations by updating only the affected parts while maintaining exactness.

Contribution

It presents a novel streaming assembly technique that enables efficient, exact updates in topologically dynamic tetrahedral mesh simulations, outperforming full rebuilds.

Findings

Achieves 1.37x to 1.61x speedup over full-rebuild methods.

Reduces matrix update costs by orders of magnitude.

Up to 76% speedup in fracture simulation frames with exact results.

Abstract

Dynamic tetrahedral simulation pipelines rebuild topology-dependent solver state after every fracture, refinement, or merge event - discarding structural continuity that survives each edit and spending global work on what are often local changes. We present STA-FEM, a streaming assembly method for simulations with topologically-dynamic tetrahedral meshes operating on a fixed superset mesh: when the candidate element pool is preallocated and the per-frame edit stream is exposed, the surrounding solver, preconditioner, and time-stepping layers stay unchanged while the per-frame assembly step is replaced with persistent incremental updates that match a full-rebuild approach exactly at every frame. Across various three-dimensional examples with up to 460k elements, the method delivers end-to-end speedups of 1.37x to 1.61x over full-rebuild with orders-of-magnitude reductions in matrix update cost, preserving exact matrix parity in all tested frames against a stronger exact local recomputation baseline. We test our algorithm in realistic fracture simulation pipelines and observe up to 76% speedups in fracture frame time with exact equivalence to a ground-truth full-rebuild algorithm. These results establish exact streaming assembly as a potentially practical approach for simulating tetrahedral meshes with dynamic topology.