论文标题
Nitsche未固定的方法用于计算具有杂质的音调晶体中的带结构
Unfitted Nitsche's method for computing band structures in phononic crystals with impurities
论文作者
论文摘要
在本文中，我们提出了一种未固定的Nitsche方法，以计算具有一般几何杂质的语音晶体的带状结构。所提出的方法不需要背景网格安装杂质的接口，从而避免了产生身体构成网格的昂贵成本，并简化了将界面条件纳入公式中的昂贵成本。准周期边界条件是通过Floquet-Bloch变换来处理的，该变换将带状结构的计算转换为具有周期性边界条件的特征值问题。更重要的是，我们使用基于痕量不平等的微妙论点来展示提出方法的良好性，并进一步证明Babuška-osborn理论的收敛性。我们在存在一般几何形状杂质的情况下达到最佳收敛速率。我们通过两个数值示例确认了理论结果，并显示了所提出的方法计算带结构的能力，而无需拟合杂质的界面。
In this paper, we propose an unfitted Nitsche's method to compute the band structures of phononic crystal with impurities of general geometry. The proposed method does not require the background mesh to fit the interfaces of impurities, and thus avoids the expensive cost of generating body-fitted meshes and simplifies the inclusion of interface conditions in the formulation. The quasi-periodic boundary conditions are handled by the Floquet-Bloch transform, which converts the computation of band structures into an eigenvalue problem with periodic boundary conditions. More importantly, we show the well-posedness of the proposed method using a delicate argument based on the trace inequality, and further prove the convergence by the Babuška-Osborn theory. We achieve the optimal convergence rate at the presence of the impurities of general geometry. We confirm the theoretical results by two numerical examples, and show the capability of the proposed methods for computing the band structures without fitting the interfaces of impurities.
