Frozen Gaussian approximation for high frequency wave propagation in periodic media
It addresses the computational challenge of multiscale wave propagation in periodic media for researchers in computational physics and applied mathematics.
The paper derives a frozen Gaussian approximation for high-frequency wave propagation in periodic media, establishing convergence to the true solution and enabling efficient numerical algorithms.
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].