Eulerian Gaussian beam method for high frequency wave propagation in heterogeneous media with discontinuities in one direction

Abstract. This paper generalizes the Eulerian Gaussian beam method developed in [S. Jin, H. Wu and X. Yang, Commun. Math. Sci., 6, 995–1020, 2008] to compute the high frequency wave propagation in heterogeneous media with discontinuities in one direction. The discontinuities in the wave speed correspond to the interfaces at which the incoming waves can be partially transmitted and reflected. We propose proper interface conditions to capture the reflection and transmission of Gaussian beams. These interface conditions arise naturally from an elegant combination of a Hamiltonian preserving scheme proposed in [S. Jin and X. Wen, Commun. Math. Sci., 3, 285–315, 2005] and the Eulerian Gaussian beam formulation. Numerical examples are also given to show the performance of this method.

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