TY - JOUR
T1 - Mortar DG Method with Staggered Hybridization for Rayleigh Waves Simulation
AU - Du , Jie
AU - Chung , Eric
JO - Communications in Computational Physics
VL - 1
SP - 111
EP - 127
PY - 2020
DA - 2020/11
SN - 29
DO - http://doi.org/10.4208/cicp.OA-2020-0034
UR - https://global-sci.org/intro/article_detail/cicp/18424.html
KW - Discontinuous Galerkin method, elastic wave equations, Rayleigh wave, mortar formulation, hybridization.
AB - <p style="text-align: justify;">The simulation of Rayleigh waves is important in a variety of geophysical
applications. The computational challenge is the fact that very fine mesh is necessary as the waves are concentrated at the free surface and decay exponentially away
from 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 discontinuous
Galerkin 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 coarse
mesh in most of the domain. This approach reduces the computational cost significantly. The staggered hybridization allows the preservation of the strong symmetry of
the stress tensor without complicated construction of basis functions. In particular, the
basis functions are piecewise polynomial without any continuity requirement, and the
coupling 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 demonstrate
the performance of the proposed method.</p>