A novel hybrid method based on discontinuous Galerkin method and staggered‐grid method for scalar wavefield modelling with rough topography

Abstract

In recent years, the discontinuous Galerkin method and the finite‐difference method have been widely applied to simulate seismic wave propagation. However, few studies have focused on the combination of the finite‐difference method with the discontinuous Galerkin method. We develop a new hybrid algorithm based on domain decomposition that combines the high efficiency of the finite‐difference method with the flexibility of the discontinuous Galerkin method. A computational domain is decomposed into two types of subregions where the finite‐difference method is applied in the main part of the model, whereas the discontinuous Galerkin method is employed to handle the complex structure with a free surface or caves. Total variation diminishing Runge–Kutta time discretization is used to enhance the stability of implementation. The approach inherits the advantages of the discontinuous Galerkin method and the finite‐difference method and does not need a transition zone, which reduces the computational cost caused by the additional conversion. In addition, some mesh patterns are provided to make the discontinuous Galerkin method domain discretized as needed without changing the grid size of the finite‐difference method region, which makes our hybrid algorithm more flexible. Numerical experiments prove that our hybrid scheme is capable of dealing with complex structures and maintains moderate computational efficiency.