周期介质中高频波传播的冻结高斯近似
Frozen Gaussian approximation for high frequency wave propagation in periodic media
AI总结：
本文基于布洛赫分解和相空间渐近分析，推导了周期介质中高频波传播的冻结高斯近似，并证明其收敛性，为高效数值算法提供了理论基础。
摘要：
在周期介质中高频波传播问题由于多尺度特性（短波长、小晶格常数和大物理域尺寸）而极具挑战性。传统计算方法成本极高，尤其在高维情况下更为明显。本文基于布洛赫分解和相空间渐近分析，推导了周期介质中高频波传播的冻结高斯近似，并建立了其收敛性。该方法导致了高效的数值算法，这些算法在 companion paper [Delgadillo, Lu and Yang, arXiv:1509.05552] 中进行了阐述。
英文摘要：
Propagation of high-frequency wave in periodic media is a challenging problem due to the existence of multiscale characterized by short wavelength, small lattice constant and large physical domain size. Conventional computational methods lead to extremely expensive costs, especially in high dimensions. In this paper, based on Bloch decomposition and asymptotic analysis in the phase space, we derive the frozen Gaussian approximation for high-frequency wave propagation in periodic media and establish its converge to the true solution. The formulation leads to efficient numerical algorithms, which are presented in a companion paper [Delgadillo, Lu and Yang, arXiv:1509.05552].
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
