Convergence problem of plane-wave expansion method for phononic crystals
Convergence problem of plane-wave expansion method for phononic crystals
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DOI：
10.1016/j.physleta.2004.05.030
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发表时间：
2004-06
影响因子：
2.6
通讯作者：
Yongjun Cao;Z. Hou;You-yan Liu
中科院分区：
文献类型：
--
作者：
Yongjun Cao;Z. Hou;You-yan Liu
开发了声子晶体本征问题的新公式。详细检查了能带结构计算中新公式的收敛性，并与传统平面波展开（CPWE）方法的收敛性进行了比较。数值结果表明，CPWE方法收敛缓慢并不是由于不同材料界面弹性系数（或位移场）的傅里叶级数收敛缓慢，而是由于计算中使用的特征问题的表述不恰当。数值计算还表明，对于填充分数非常高或非常低或弹性失配较大的系统，新公式可以提供比 CPWE 方法更准确的数值结果。
A new formulation of eigenproblem for phononic crystals is developed. The convergence of the new formulation in the band-structure calculations is examined in detail and compared with that of the conventional plane wave expansion (CPWE) method. Numerical results show that the slow convergence of the CPWE method is not due to the slow convergence of the Fourier series for the elastic coefficients (or displacement fields) in the interfaces of different materials, but to the inappropriate formulation of the eigenproblem used in the calculations. Numerical calculations also show that the new formulation can provide much more accurate numerical results than the CPWE method for the systems of either very high or very low filling fractions, or of large elastic mismatch.