Frozen Gaussian approximation for high frequency wave propagation in periodic media

Article type: Research Article

Authors: Delgadillo, Ricardo^a | Lu, Jianfeng^b | Yang, Xu^{a; *}

Affiliations: [a] Department of Mathematics, University of California, Santa Barbara, CA 93106, USA. E-mails: rdelgadi@math.ucsb.edu, xuyang@math.ucsb.edu | [b] Departments of Mathematics, Physics, and Chemisty, Duke University, Box 90320, Durham, NC 27708, USA. E-mail: jianfeng@math.duke.edu

Correspondence: [*] Corresponding author. E-mail: xuyang@math.ucsb.edu.

Abstract: 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 [SIAM J. Sci. Comput. 38 (2016), A2440–A2463].

Keywords: Frozen Gaussian approximation, high-freqency wave propagation, lattice potential, Bloch decomposition

DOI: 10.3233/ASY-181479

Journal: Asymptotic Analysis, vol. 110, no. 3-4, pp. 113-135, 2018