A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals
A Petrov-Galerkin finite element interface method for interface problems with Bloch-periodic boundary conditions and its application in phononic crystals
复制标题
布洛赫周期边界条件界面问题的Petrov-Galerkin有限元界面法及其在声子晶体中的应用
DOI：
10.1016/j.jcp.2019.04.051
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发表时间：
2019
影响因子：
4.1
通讯作者：
Shi Liwei
中科院分区：
文献类型：
--
作者：
Wang Liqun;Zheng Hui;Lu Xin;Shi Liwei
本文提出了一种Petrov-Galerkin有限元界面法（PGFEIM）来求解具有Bloch周期边界条件的椭圆和弹性界面问题。该方法的主要思想是选择与界面无关的标准有限元基作为检验函数基，选择一个满足跨界面跳跃条件的分段线性函数作为求解基。我们使用的网格是非贴体网格。PGFEIM能够处理具有矩阵系数和非齐次跳跃条件的锐边界面问题。进一步，我们将此方法推广到声子晶体中反平面横波和面内弹性波的能带结构的计算。不同的声阻抗比，任意复杂的散射体的几何形状和各种材料的性能被认为是和讨论。数值实验表明，该方法对界面问题具有接近二阶精度的L ∞范数，对声子晶体的能带结构计算是准确有效的.
In this paper, we propose a Petrov-Galerkin finite element interface method (PGFEIM) to solve the elliptic and elastic interface problems with Bloch-periodic boundary conditions. The main idea of this method is to choose the standard finite element basis independent of the interface to be the test function basis, and choose a piecewise linear function satisfying the jump conditions across the interface to be the solution basis. The grid we use is a non-body-fitted grid. The PGFEIM is capable of dealing with sharp-edged interface problems with matrix coefficients and nonhomogeneous jump conditions. Further, we extend this method to compute the band structure of anti-plane transverse waves and in-plane elastic waves in phononic crystals. Different acoustic impedance ratios, arbitrary complex scatterer geometries and various material properties are considered and discussed. Numerical experiments demonstrate that the PGFEIM is nearly second order accurate in the L∞ norm for interface problems, and it is accurate and efficient for computing the band structure of phononic crystals.