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

2026-05-12

AI Summary

This work addresses the high computational overhead incurred when dynamically edited tetrahedral meshes—subject to topological changes such as fracture, refinement, or merging—require full recomputation of solver states. The authors propose an exact streaming assembly method that leverages a pre-allocated superset mesh and a known sequence of edits to enable persistent incremental updates, thereby replacing global reassembly. This approach yields results mathematically equivalent to full reconstruction while preserving the solver, preconditioner, and time-stepping scheme unchanged. By maintaining structural continuity in unaffected regions, the method drastically reduces redundant computation. Experiments on 3D scenes with up to 460k elements demonstrate matrix update costs reduced by several orders of magnitude, end-to-end speedups of 1.37–1.61×, and up to a 76% reduction in per-frame simulation time for fracture scenarios—all without any deviation from baseline accuracy.

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.

Problem

• dynamic topology
• tetrahedral mesh
• simulation
• matrix assembly
• fracture simulation

Innovation

• streaming assembly
• dynamic tetrahedral topology
• exact incremental update
• preallocated superset mesh
• fracture simulation