System and a method for numerical simulation of wave propagation in homogeneous media

摘要

The present invention provides a method to construct stable, high-order explicit discretization for the wave equation based on the discretization of the evolution formula. The present invention provides independent computation of discretization in one, two, or more spaces for bulk propagation, near boundaries propagation, and discretization of a projection operator to enforce boundary conditions. More specifically, the method includes an act of discretizing propagation operators L_Δt by using an identity that is derived using central differencing in time. The method also includes an act of providing a high-order discretization of a boundary projection operator that enforces boundary conditions independent of the discretization of the propagation operators L_Δt. Additionally, the method includes an act of alternating an application of a discretization of an evolution formula having a spatial filtering operator L_Δt with a boundary projection operation for stepping forward in time to determine wave propagation in the media.