Graduate and Postdoctoral Studies
Computational and Applied Mathematics
GPU-accelerated discontinuous Galerkin methods on hybrid meshes: applications in seismic imaging
Monday, March 27, 2017
to 3:00 PM
1064 Duncan Hall
I present a discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation and its application in seismic imaging.
Discontinuous Galerkin methods are a class of numerical methods for solving partial differential equations. The ability to work on unstructured meshes allows DG to handle complex geometry. The independence of element-wise operations makes DG schemes easy to be parallelized and hence suitable for large-scale computations.
In this thesis, a DG solver is built on hybrid meshes containing hexahedra, tetrahedra, prisms, and pyramids. Computational efficiency and accuracy are achieved through the use of hex-dominant meshes. The computational speed is further improved by a combination of element-specific kernels, multiple graphics processing units (GPUs) acceleration and multi-rate time stepping.
The applications of the DG methods in reverse time migration (RTM) and full waveform inversions (FWI) are studied and validated with test cases. Special DG properties are taken into considerations in the seismic applications. In particular, sharp interfaces of velocity models are inverted with the help of surface integration of image and mesh regeneration at each FWI iteration.