Graduate and Postdoctoral Studies
Computational and Applied Mathematics
Energy-conserving Composite-Grid Finite-Difference Time-Domain Scheme for Elastic Wave Simulations
Friday, March 24, 2017
to 12:00 PM
3076 Duncan Hall
Finite-difference time-domain (FDTD) scheme is one of the most widely used schemes for seismic wave simulations. However, FDTD suffers from the grid dispersion problem. To mitigate this numerical artifact, the grid spacing used for FDTD needs to be small enough so that all the wavelengths of the propagating waves are sampled beyond a certain ratio. Therefore, if the simulation region presents strong velocity variations, then using a uniform-grid FDTD scheme (UGS) is computationally inefficient as a fine grid has to be built over the entire simulation region.
To solve this inefficiency, I propose an energy-conserving composite-grid FDTD scheme (EC-CGS) based on the first-order elastic wave equation system. The composite-grid configuration allows EC-CGS to use a fine grid on the low-velocity region and a coarse grid on the high-velocity region. Meanwhile, the energy-conserving property ensures numerical stability for EC-CGS provided that the time step meets a certain constraint of CFL type. A key step in deriving EC-CGS is to update the data near the grid refinement interface by solving linear equation system(s) derived from the energy-conserving property and the physical transmission condition across the grid refinement interface; this step to updating the interface data distinguishes EC-CGS from the rest of the composite-grid FDTD schemes. Numerical results of 1-D/3-D wave simulations demonstrate the energy-conserving property, stability and convergence of EC-CGS. In particular, EC-CGS solutions agree well with UGS solutions even when strong heterogeneity is present across the grid interface, although EC-CGS uses a coarser grid on part of the computational domain and thereby takes less run time and needs less memory.