Section: New Results

Numerical Analysis

Fourth-order energy-preserving locally implicit discretization for linear wave equations

Participants : Juliette Chabassier [Magique-3d] , Sébastien Imperiale [correspondant] .

A family of fourth-order coupled implicit-explicit time schemes has been developed. The spatial coupling is done at the boundaries of several non conforming meshes of regions in which we want to simulate propagating waves. A global discrete energy is shown to be preserved and leads to global fourth-order consistency. Numerical results in 1D and 2D have been produced to illustrate the good behavior of the schemes and their potential for the simulation of realistic highly heterogeneous media and strongly refined geometries, for which using an explicit scheme everywhere can be extremely penalizing. Accuracy up to fourth order reduces the numerical dispersion inherent to implicit methods used with a large time step, and makes this family of schemes attractive compared to second order accurate methods in time.