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 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：质量集中技术常用于结构动力学问题的显式时间积分方案，既能避免求解与一致质量矩阵相关的昂贵线性系统，又能提高临界时间步长。在等几何分析中，临界时间步长受所谓“异常”频率的限制，这些频率代表了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。本研究针对非平凡几何（包括多片几何与裁剪几何）提出了质量集中与异常频率消除技术。所提出的集中策略被证明不会恶化（且通常会改善）原始问题的CFL条件，并结合收缩技术以消除持续存在的异常频率。数值实验验证了该方法的优势，特别是在长时间跨度的仿真中，可在几乎不影响数值解的前提下将迭代次数减少一半。