A superconvergent cross element integration technique is presented for the cubic isogeometric formulation referring to the frequency computation of wave equations. More specifically, a four-element integration cell with 11-point quadrature and an intermediate two-element integration cell with 6-point quadrature are developed in accordance with the optimization of discrete isogeometric frequency error. These cross-element quadrature rules stand in sharp contrast to the conventional 4-point element based integration for the cubic isogeometric formulation, which needs 16 quadrature points within four elements per spatial dimension, especially for multi-dimensional scenarios. Meanwhile, a superconvergence with two added accuracy orders upon the 6th order accurate standard cubic isogeometric approach is naturally embedded in the proposed cross element integration technique by construction. Consequently, both efficiency and accuracy advantages are simultaneously realized in the proposed cross element integration method for cubic isogeometric formulation. The efficacy of the proposed superconvergent methodology is consistently validated by several representative numerical examples.

中文翻译：

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使用三次等几何公式进行超收敛频率计算的交叉元积分

参考波动方程的频率计算，提出了三次等几何公式的超收敛交叉元积分技术。具体而言，根据离散等几何频率误差的优化，开发了11点正交的四元件积分单元和6点正交的中间二元件积分单元。这些跨元素求积规则与立方等几何公式的传统基于 4 点元素的积分形成鲜明对比，后者在每个空间维度的四个元素内需要 16 个求积点，特别是对于多维场景。同时，在六阶精确标准立方等几何方法的基础上增加两个精度阶的超收敛通过构造自然地嵌入到所提出的跨单元积分技术中。因此，所提出的三次等几何公式的交叉元素积分方法同时实现了效率和精度优势。所提出的超收敛方法的有效性得到了几个代表性数值例子的一致验证。