关于DEIM子空间在投影动力学非线性力约简中的兼容性

中文摘要 AI 辅助

在基于物理的模拟中，非线性约束力的评估是计算复杂性的主要来源。在投影动力学框架内，求解器在估计这些力与更新下一帧的顶点位置之间交替进行。本研究探讨了基于快照的子空间方法在保持非线性动力学保真度的同时加速约束项计算的潜力。我们特别关注离散经验插值方法（DEIM），考察其能否识别出一组约简的约束网格单元，从而实现对全系统力的精确插值与近似。我们的实验表明，DEIM在约束投影约简方面既不直观也并非始终有效。尤其是当约束涉及多个顶点时，其性能会退化。为验证这些观察结果，我们展示了在三维嵌入的表面网格和体积网格上全阶与约简阶模拟之间的比较。此外，我们报告了各类约束的重构误差，为该方法在此情境下的局限性提供了定量证据。

英文摘要

In physics-based simulations, the evaluation of nonlinear constraint forces represents a primary source of computational complexity. Within the framework of projective dynamics, the solver alternates between estimating these forces and updating vertex positions for the subsequent frame. This work investigates the potential of snapshot-based subspace methods to accelerate the computation of constraint terms while maintaining the fidelity of nonlinear dynamics. We focus specifically on the Discrete Empirical Interpolation Method (DEIM), examining whether it can identify a reduced set of constrained mesh elements that enable accurate interpolation and approximation of forces across the full system. Our experiments demonstrate that DEIM is neither intuitive nor consistently effective for constraint projection reduction. In particular, its performance degrades when constraints involve multiple vertices. To validate these observations, we present comparisons between full-order and reduced-order simulations on both surface meshes embedded in three dimensions and volumetric meshes. Furthermore, we report reconstruction errors for various classes of constraints, providing quantitative evidence of the method limitations in this context.

发表机构

• Max Planck Institute for Dynamics of Complex Technical Systems（马克斯·普朗克复杂技术系统动力学研究所）
• Otto-von-Guericke Universität（奥托·冯·格里克大学）

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