MIISO：用于等几何离群值稳定的模态积分器
MIISO: Modal Integrators for Isogeometric Stabilization of Outliers
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- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校奥登计算工程与科学研究所）
- Department of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin（德克萨斯大学奥斯汀分校航空航天工程与应用力学系）
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中文总结 AI 辅助
本文提出MIISO，一种通过时间积分抑制等几何离散化中非物理离群模态的指数Rosenbrock-Krylov积分器族，无需修改空间离散化，高效可扩展，且无条件稳定并具有高阶收敛性。
中文摘要 AI 辅助
高阶等几何离散化在离散谱的顶部会产生少量非物理的离群模态。这些模态会污染波动传播和结构动力学中的数值解。大多数现有的补救措施通过无离群基、质量集中、子空间投影和其他方法修改空间离散化。我们引入了MIISO（用于等几何离群值稳定的模态积分器），这是一族指数Rosenbrock-Krylov积分器，它们在时间上抑制离群模态，同时保持空间离散化不变。该方法识别离群值并修改时间积分方案以消除它们，同时保持物理模态无耗散。这些积分器通过Krylov近似以无矩阵方式评估，使其高效且可扩展。虽然是为等几何分析开发的，但该机制可扩展到任何可以表征谱病理的方法。该族是无条件A稳定的，并在二阶、三阶和四阶全局收敛，且可扩展到非线性问题。数值实验在各种等几何问题上与其他时间积分方法相比，确认了预期的离群值和物理模态行为，并表明MIISO在不改变离散化的情况下匹配了之前的空间离群值去除。它们还恢复了预测的收敛阶，并在匹配精度下显示出比广义-alpha更低的成本。
英文摘要
High-order isogeometric discretizations produce a small number of non-physical outlier modes at the top of the discrete spectrum. These modes can pollute the numerical solution in wave propagation and structural dynamics. Most existing remedies modify the spatial discretization through outlier-free bases, mass lumping, subspace projection, and other methods. We introduce MIISO (Modal Integrators for Isogeometric Stabilization of Outliers), a family of exponential Rosenbrock-Krylov integrators that suppress outlier modes temporally while leaving the spatial discretization unmodified. The method identifies the outliers and modifies the time-integration scheme to annihilate them while leaving physical modes without dissipation. The integrators are evaluated matrix-free through Krylov approximation, making them efficient and scalable. While developed for isogeometric analysis, the mechanism extends to any method in which a spectral pathology can be characterized. The family is unconditionally A-stable and globally convergent at orders two, three, and four, and it extends to nonlinear problems. Numerical experiments confirm the intended outlier and physical mode behavior on a variety of isogeometric problems compared to other time integration methods, and show that MIISO matches previous spatial outlier removal without changing the discretization. They also recover the predicted convergence orders and show lower cost than generalized-alpha at matched accuracy.
