发表机构
The University of Melbourne; Shanghai Jiao Tong University; Southern University of Science and Technology（墨尔本大学; 上海交通大学; 南方科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出TOGEARI方法对带IPC接触的凝聚有限元系统的接触更新做因子空间压缩，实验在325260自由坐标的冻结系统中验证其可减少Arnoldi基向量数量与求解时间，同时指出若干待解决问题。
AI 中文摘要
凝聚有限元接触系统结合了大型材料体积核心与薄的因式化接触更新。我们提出了相关交互的截断算子-格拉姆特征空间近似（TOGEARI），这是对该更新的因子空间压缩方法。它选择低维接触组合空间，并将其贡献作为Woodbury右预处理因子安装。组装的牛顿方程和独立残差测试保持固定，逆作用需要可逆核心和简化的Woodbury系统。核心响应选择额外假设核心对称，当核心不定时仍可用；对于正定核心，响应值具有能量排序，相同分析随后给出精确广义谱、缩放逆误差恒等式以及每一维度下最优的最劣省略交互。原始接触因子选择器提供了设置成本更低的经验替代方案。我们推导了二次四面体位移格式的拆分，该格式具有局部凝聚的单元常数压力和因式化的半正定IPC法向切线。在具有325260个自由坐标的冻结系统中，94行接触因子的8维子空间（已注册数值秩为42）将Arnoldi基向量从11个减少到5个。核心响应空间和原始空间在主要及近重复提取上紧密对齐；行范数和确定性随机控制需要12个向量。保留维度扫描将热中位数时间从2.849秒减少到1.629秒，加载后设置加首次求解时间从53.885秒变为61.958秒。这些结果在一个冻结、无摩擦的 regime中识别出紧凑的交互修正，不同牛顿状态、演化接触、接触秩和网格缩放、摩擦以及嵌套压力空间性能仍是待解决的实验问题。
英文摘要
TOGEARI constructs a compressed contact correction for condensed finite-element equations with incremental potential contact (IPC). A core-conditioned interaction matrix ranks contact combinations by their mechanical responses; a raw-factor proxy acquires only the retained responses. For a symmetric positive-definite core, the reference analysis gives the exact spectrum, scaled inverse error and optimal worst omitted interaction. The selected responses are maintained through signed contact changes using supported operator images and a small coarse matrix. A complementary Schur spectrum and perturbation bounds connect this construction to the full current linear equation, damped local Newton steps and compatible episode reuse. On a 325,260-coordinate finger/cup problem, eight selected directions reduce Krylov work from eleven columns to five, matching full contact. Two reversed-order load studies give matching anchored displacements and accepted normal reactions, with 28.8-29.3 percent less warm time and 5.1-5.3 percent less complete time than per-step direct refactorization. A completed twelve-episode run saves 18.8 percent of total time against direct and 2.8 percent against a held factor. Full response caching has comparable time with 7.5 times the response storage. A compressed repeat terminates at an energy line search; separate diagnostics identify constitutive cancellation and terminal-backtracking sensitivity. Larger-contact, held-out-load and frictional comparisons show where compression or preparation loses its advantage. The complete Newton equation remains the residual operator throughout; the convergence guarantees retain their stated reference and local hypotheses.
Comments45 pages, 4 figures
