# A ray-based IPDG method for high-frequency time-domain acoustic wave propagation in inhomogeneous media

## TL;DR

This paper introduces a ray-based IPDG method for high-frequency acoustic wave simulation in inhomogeneous media, achieving higher accuracy and stability with fewer unknowns compared to traditional methods.

## Contribution

The proposed method combines geometrical optics-inspired basis functions with wavefront tracking to improve high-frequency wave simulation accuracy in inhomogeneous media.

## Key findings

- Significantly higher accuracy than polynomial-based IPDG methods
- Moderate growth of relative errors with increasing frequency
- Effective dimension reduction and wavefront tracking

## Abstract

The numerical approximation of high-frequency wave propagation in inhomogeneous media is a challenging problem. In particular, computing high-frequency solutions by direct simulations requires several points per wavelength for stability and usually requires many points per wavelength for a satisfactory accuracy. In this paper, we propose a new method for the acoustic wave equation in inhomogeneous media in the time domain to achieve superior accuracy and stability without using a large number of unknowns. The method is based on a discontinuous Galerkin discretization together with carefully chosen basis functions. To obtain the basis functions, we use the idea from geometrical optics and construct the basis functions by using the leading order term in the asymptotic expansion. Also, we use a wavefront tracking method and a dimension reduction procedure to obtain dominant rays in each cell. We show numerically that the accuracy of the numerical solutions computed by our method is significantly higher than that computed by the IPDG method using polynomials.Moreover, the relative errors of our method grow only moderately as the frequency increases.