Mortar DG Method with Staggered Hybridization for Rayleigh Waves Simulation (Communications in Computational Physics, 2020)
The simulation of Rayleigh waves is important in a variety of geophysicalapplications. The computational challenge is the fact that very fine mesh is necessary as the waves are concentrated at the free surface and decay exponentially awayfrom the free surface. To overcome this challenge and to develop a robust high order scheme for the simulation of Rayleigh waves, we develop a mortar discontinuousGalerkin method with staggered hybridization. The use of the mortar technique allows one to use fine mesh in only a local region near the free surface, and use coarsemesh in most of the domain. This approach reduces the computational cost significantly. The staggered hybridization allows the preservation of the strong symmetry ofthe stress tensor without complicated construction of basis functions. In particular, thebasis functions are piecewise polynomial without any continuity requirement, and thecoupling of the basis functions is performed by using carefully chosen hybridized variables. The resulting scheme is explicit in time, and only local saddle point system is solved for each time step. We will present several benchmark problems to demonstratethe performance of the proposed method.
Keywords: Discontinuous Galerkin method; elastic wave equations; Rayleigh wave; mortar formulation; hybridization.