Mass lumping techniques are commonly employed in explicit time integration schemes for problems in structural dynamics and both avoid solving costly linear systems with the consistent mass matrix and increase the critical time step. In isogeometric analysis, the critical time step is constrained by so-called "outlier" frequencies, representing the inaccurate high frequency part of the spectrum. Removing or dampening these high frequencies is paramount for fast explicit solution techniques. In this work, we propose robust mass lumping and outlier removal techniques for nontrivial geometries, including multipatch and trimmed geometries. Our lumping strategies provably do not deteriorate (and often improve) the CFL condition of the original problem and are combined with deflation techniques to remove persistent outlier frequencies. Numerical experiments reveal the advantages of the method, especially for simulations covering large time spans where they may halve the number of iterations with little or no effect on the numerical solution.

翻译：质量集中技术常被用于结构动力学问题的显式时间积分方案中，既可避免求解与一致质量矩阵相关的昂贵线性系统，又能增大临界时间步长。在等几何分析中，临界时间步长受限于所谓"离群"频率，即频谱中不准确的高频部分。消除或抑制这些高频成分对于快速显式求解技术至关重要。本文针对非平凡几何（包括多片几何和裁剪几何）提出了鲁棒的质量集中与离群频率消除技术。理论上证得，所提出的集中策略不会降低（通常能改善）原始问题的CFL条件，并与压缩技术相结合以消除持续存在的离群频率。数值实验揭示了该方法的优势，尤其对于覆盖大时间跨度的模拟，该方法可在对数值解影响甚微甚至无影响的情况下将迭代次数减半。