The Eulerian Gaussian beam method for high frequency wave propagation in the reduced momentum space

• Generalize the Eulerian Gaussian beam method for high frequency wave propagation.
• Derive the new formulation of Hessian function in the reduced momentum space.
• Present numerical examples to show the performance of the method.

The Eulerian Gaussian beam method is an efficient way to compute high frequency wave propagation, which was originally studied in Leung et al. (2007) [17]. Later Jin, Wu and Yang developed a new way of computing the Hessian functions from the derivatives of the level set functions in Jin et al. (2008) [19], which greatly reduced the number of equations in the Eulerian Gaussian beam method.In this paper, we generalize this new method (JWY-EGBM) to compute high frequency wave propagation in the reduced momentum space. The difficulty lies in that, the dimensionality of momentum space is one less than that of configuration space, while JWY-EGBM requires configuration and momentum spaces be equally dimensional. We present two numerical examples to show the performance of the proposed method.