An Efficient Local Time-Stepping Scheme for Discontinuous Galerkin Multi-scale Modeling

This paper presents a local time-stepping technique that uses different time steps based on the mesh density. By evaluating the diameters of the inscribed spheres of the meshes, the maximum allowable time step for each mesh is determined. This method effectively improves simulation efficiency, especially for models with multiscale structures, significantly reducing the consumption of computational resources and simulation time. The same numerical example was tested for both global and local time-stepping to compare computation durations, and the results show that, compared to global time-stepping scheme, local time-stepping scheme improved computation efficiency by 150 times.