A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies and eigenmodes. For degree two and higher, however, optical branches of spurious outlier frequencies and modes may appear due to boundaries or reduced continuity at patch interfaces. In this paper, we introduce a variational approach based on perturbed eigenvalue analysis that eliminates outlier frequencies without negatively affecting the accuracy in the remainder of the spectrum and modes. We then propose a pragmatic iterative procedure that estimates the perturbation parameters in such a way that the outlier frequencies are effectively reduced. We demonstrate that our approach allows for a much larger critical time-step size in explicit dynamics calculations. In addition, we show that the critical time-step size obtained with the proposed approach does not depend on the polynomial degree of spline basis functions.

翻译：等离子化的主要优点是其准确和行为良好的偏差元和偏差模式。但是,在二级和更高一级,虚假的外部频率和模式的光学分支可能由于边界或补丁界面的连续性降低而出现。在本文中,我们采用了基于隔热的单值分析的变式方法,消除异差频率而不会对频谱和模式其余部分的准确性产生不利影响。然后,我们提出一个务实的迭代程序,以有效减少外差频率的方式估计扰动参数。我们证明,我们的方法允许在明确的动态计算中采用更大的关键时间步骤尺寸。此外,我们表明,采用拟议方法获得的关键时间步骤大小并不取决于多角度基函数的多度。