Application of Nodal Discontinuous Glaerkin Methods in Acoustic Wave Modeling

This work will explore the discontinuous Galerkin finite element method (DG-FEM) for solving acoustic wave equations in heterogeneous material. High order convergence of DG-FEM will be verified by examples. The numerical error using DG-FEM has the same components as using finite-difference method: grid dispersion and misalignment between numerical grids and material interfaces. Both error components can be reduced by high order schemes and mesh techniques respectively as I expect. The numerical experiments suggest two possible techniques to eliminate the error component associated with the mesh misalignment. The absorbing boundary conditions are implemented for infinite or semi-infinite domain problems. Plane wave as well as point source wave experiments are constructed to make validity and convergence tests of DG. INTRODUCTION In physics, the acoustic wave equation, governing the acoustic wave propagation through material media, describes the evolution of acoustic pressure and particle velocity as a function of space and time. Seismologists gain the knowledge of geological structure of subsurface by sending seismic waves and recording the reflected wave. Inversion of these recorded data is essential for geoscientists to understand the mystery under the surface of earth. In each inversion process, many forward wave propagation problems need to be solved. So accurately and efficiently solving acoustic wave equation is the first step for constructing an inverse solver. FDTD for simulation of acoustic wave propagation have been studied by (Alford et al., 1974(2); Alterman and Karal, 1968(3); Boore, 1970(5), 1972(6); Dablain, 1986(8); Kelly et al., 1976(11)). There are many successful implementations of FDTD within seismic applications. Among them, the very recent software iwave by (Igor Terentyev, 2008(15)), providing a parallel framework using staggered-grid finite difference method, sets up an instrument for comparing FDTD with other numerical methods. DG-FEM has recently become popular for fluid dynamics and electromagnetic problems