Improving the generalized Bloch mode synthesis method using algebraic condensation
Improving the generalized Bloch mode synthesis method using algebraic condensation
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DOI：
10.1016/j.cma.2021.113758
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发表时间：
2021-06
影响因子：
7.2
通讯作者：
Chenyang Xi;Hui Zheng
中科院分区：
文献类型：
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作者：
Chenyang Xi;Hui Zheng
广义布洛赫模综合（GBMS）是一种有效的模型降阶技术，可以减少周期介质能带结构计算的计算量。在这篇文章中，试图提高GBMS方法的计算性能，采用代数凝聚（AC）。首先在代数域中将单胞的内部分量自动划分为一组小子结构，然后利用改进的约化系统（IRS）方法将这些子结构吸收到边界集合中。边界自由度（DOF）随后分别通过增强的Craig-Bampton（ECB）方法和局部水平特征约束模态约简进行约简。在Bloch边界条件的作用下，对IRS和ECB过程的耦合余模进行了补偿。通过几个数值例子，所提出的方法的性能表现在精度和计算成本。最后讨论了分区数对算法计算效率的影响。数值结果表明，对于自由度较大或外边界网格密集的单元格，采用AC可以大大提高GBMS方法的计算效率，从而扩展了GBMS方法的应用范围。
The generalized Bloch mode synthesis (GBMS) is an efficient model-order reduction technique to reduce the computational cost for band-structure calculations of periodic media. In this article, an attempt is made to improve the computational performance of the GBMS method by employing algebraic condensation (AC). The interior component of the unit cell is firstly partitioned into a set of small substructures automatically in the algebraic domain, and these substructures are then absorbed into boundary sets by using the improved reduced system (IRS) method. The boundary degrees of freedom (DOFs) are subsequently reduced via the enhanced Craig–Bampton (ECB) method and the local-level characteristic constraint mode reduction, respectively. The coupling residual modes of IRS and ECB processes are then compensated after imposing the Bloch boundary conditions. Through several numerical examples, the performance of the proposed method is demonstrated in terms of accuracy and computational cost. The influence of partitioned numbers on the computational efficiency of the proposed method is finally discussed. The numerical results show that the computational efficiency of the GBMS method can be greatly enhanced by using AC for the unit cells with relatively large DOFs or with dense meshes of the exterior boundary, which hence extends the application scope of the GBMS method.