Frozen Gaussian approximation (FGA) has been applied and numerically verified as an efficient tool to compute high-frequency wave propagation modeled by non-strictly hyperbolic systems, such as the elastic wave equations [J.C. Hateley, L. Chai, P. Tong and X. Yang, Geophys. J. Int., 216:1394–1412, 2019] and the Dirac system [L. Chai, E. Lorin and X. Yang, SIAM J. Numer. Anal., 57:2383–2412, 2019]. However, the theory of convergence is still incomplete for non-strictly hyperbolic systems, where the latter can be interpreted as a diabatic (or more) coupling. In this paper, we establish the convergence theory for FGA for linear non-strictly hyperbolic systems, with an emphasis on the elastic wave equations and the Dirac system. Unlike the convergence theory of FGA for strictly linear hyperbolic systems, the key estimate lies in the boundedness of intraband transitions in diabatic coupling.

中文翻译：

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线性非严格双曲系统的冻结高斯逼近的收敛性

冻结高斯近似（FGA）已被应用并进行了数值验证，作为计算由非严格双曲系统建模的高频波传播的有效工具，例如弹性波方程[JC Hateley，L。Chai，P。Tong和X杨，地球物理 J.国际 ，216：1394–1412，2019]和Dirac系统[L. Chai，E。Lorin和X. Yang，SIAM J. Numer。肛门，57：2383–2412，2019]。但是，对于非严格双曲系统，其收敛理论仍然不完整，其中非双曲系统可以解释为非绝热（或更多）耦合。在本文中，我们建立了线性非严格双曲系统FGA的收敛理论，重点是弹性波方程和Dirac系统。与严格线性双曲系统的FGA收敛理论不同，关键的估计在于非绝热耦合中带内跃迁的有界性。