It is well-known that outliers appear in the high-frequency region in the approximate spectrum of isogeometric analysis of the second-order elliptic operator. Recently, the outliers have been eliminated by a boundary penalty technique. The essential idea is to impose extra conditions arising from the differential equation at the domain boundary. In this paper, we extend the idea to remove outliers in the superconvergent approximate spectrum of isogeometric analysis with optimally-blended quadrature rules. We show numerically that the eigenvalue errors are of superconvergence rate $h^{2p+2}$ and the overall spectrum is outlier-free. The condition number and stiffness of the resulting algebraic system are reduced significantly. Various numerical examples demonstrate the performance of the proposed method.

翻译：众所周知,在高频区域,对二阶椭圆操作员的等离子分析的近似等离子谱中出现了高频区域的外部线。 最近,通过边界处罚技术消除了外部线。 基本想法是在域边界上实行差异方程产生的额外条件。 在本文中,我们扩展了用最佳混合二次规则来清除超相异谱的异子分析近似频谱的外部线的想法。 我们用数字显示,电子值错误是超趋同率$h ⁇ 2p+2},而总体范围是无异的。 由此产生的代数系统的条件数和严谨度大大降低。 各种数字例子显示了拟议方法的性能。