Volume 29, Issue 1
Mortar DG Method with Staggered Hybridization for Rayleigh Waves Simulation

Jie DuEric Chung

Commun. Comput. Phys., 29 (2021), pp. 111-127.

Published online: 2020-11

Preview Full PDF 157 2755
Export citation
  • Abstract

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.

  • Keywords

Discontinuous Galerkin method, elastic wave equations, Rayleigh wave, mortar formulation, hybridization.

  • AMS Subject Headings

65M32, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-29-111, author = {Du , Jie and Chung , Eric}, title = {Mortar DG Method with Staggered Hybridization for Rayleigh Waves Simulation}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {1}, pages = {111--127}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0034}, url = {http://global-sci.org/intro/article_detail/cicp/18424.html} }
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 -

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.

Jie Du & Eric Chung. (2020). Mortar DG Method with Staggered Hybridization for Rayleigh Waves Simulation. Communications in Computational Physics. 29 (1). 111-127. doi:10.4208/cicp.OA-2020-0034
Copy to clipboard
The citation has been copied to your clipboard