论文标题
在源期限的周期性介质中，波动方程的收敛低波动，高频均质化
A convergent low-wavenumber, high-frequency homogenization of the wave equation in periodic media with a source term
论文作者
论文摘要
我们在定期介质中，在源术语中，其频率位于频带间隙内，我们追求低波动，二阶均质化解决方案。考虑到无界介质$ \ mathbb {r}^d $（$ d \ geqslant1 $）中的波动运动，我们首先使用（floquet-）bloch变换来在有限域中提出等效的变分问题。通过研究源术语对某些周期函数的投影，可以通过Bloch征函数的渐近扩展和地隐色分散关系来得出二阶模型。我们建立了二阶均质化解决方案的收敛性，并包括数值示例以说明收敛结果。
We pursue a low-wavenumber, second-order homogenized solution of the time-harmonic wave equation at both low and high frequency in periodic media with a source term whose frequency resides inside a band gap. Considering the wave motion in an unbounded medium $\mathbb{R}^d$ ($d\geqslant1$), we first use the (Floquet-)Bloch transform to formulate an equivalent variational problem in a bounded domain. By investigating the source term's projection onto certain periodic functions, the second-order model can then be derived via asymptotic expansion of the Bloch eigenfunction and the germane dispersion relationship. We establish the convergence of the second-order homogenized solution, and we include numerical examples to illustrate the convergence result.
