Implementation of perfectly matched layer (PML) boundary condition for curvilinear grids in the SPECFEM3D package
Abstract
The SPECFEM3D_GLOBE package (Komatitsch & Tromp 2002ab) has been widely used for global and continental-scale seismic wave simulation. While the SPECFEM3D package (Komatitsch et al. 2004) is mostly used for regional- and local-scale simulations, it is also capable of efficient continental-scale simulations with the aid of the Cube2sph toolkit (Liu et al. 2019) for mesh generation. In regional- and local-scale simulations, the mesh for simulation domain needs to be truncated at artificial boundaries, where absorbing boundary conditions are imposed to absorb outgoing waves and suppress artificial reflections. The first-order Stacey absorbing boundary condition (Clayton & Engquist 1977), which does not need additional computational cost and can accommodate arbitrary boundary geometry, is used by default in SPECFEM3D_GLOBE and SPECFEM3D. However, waves at grazing incidence cannot be effectively absorbed with the Stacey boundary condition. On the other hand, the perfectly matched layer (PML, Berenger 1994) is known to be effective even at grazing incidence, although with increased computational cost and storage. The current implementation of PML in SPECFEM3D requires the artificial boundaries to be perpendicular to the coordinate axes, and thus cannot be applied to continental-scale simulations where elements need to be deformed to accommodate the Earth's curvature.
In this study, we use coordinate transformation to derive an auxiliary differential equation (ADE) PML formulation in curvilinear grids and further formulate it into the weak form for implementation in SPECFEM3D. A velocity-stress formulation and a second-order staggered scheme (Festa & Vilotte 2005) is used for time stepping. The simulation can become unstable in the PML domain when elements are severely deformed. We hence include the multi-axial PML (MPML, Meza-Fajardo & Papageorgiou 2008) technique to stabilize the simulation. We show that the computational cost is increased by three times in the PML domain, but the increase of the total computational cost can be significantly reduced by proper load balancing with SCOTCH (Pellegrini & Roman 1996). Combining the Cube2sph toolkit and the curvilinear PML utility, continental-scale seismic wave simulations can be done efficiently and accurately with the SPECFEM3D package.- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2020
- Bibcode:
- 2020AGUFMS064.0009L
- Keywords:
-
- 3225 Numerical approximations and analysis;
- MATHEMATICAL GEOPHYSICS;
- 3260 Inverse theory;
- MATHEMATICAL GEOPHYSICS;
- 7260 Theory;
- SEISMOLOGY;
- 7290 Computational seismology;
- SEISMOLOGY