Discontinuous Galerkin Time Domain Methods for Acoustics and Comparison with Finite Difference Time Domain Methods

This thesis describes an implementation of the discontinuous Galerkin finite element time domain (DGTD) method on unstructured meshes to solve acoustic wave equations in discontinuous media. In oil industry people use finite difference time domain (FDTD) methods to compute solutions of time domain wave equations and simulate seismic surveys, the first step to explore oil and gas in the earth’s subsurface, conducted either in land or sea. The results in this thesis indicate that the first order time shift effect resulting from misalignment between numerical meshes and material interfaces in the DGTD method occurs the same way as interface errors in the finite difference simulation of wave propagation. This thesis describes two approaches: interface-fitting mesh and local mesh refinement, without modifying the DGTD scheme, to decrease this troublesome effect with verifications of 2D examples. The comparison in this thesis between the DGTD method on the piecewise linear interface-fitting mesh and the staggered FDTD method both applied to a square-circle model and a 2D dome model confirms the fact that the DGTD method can achieve a second order convergence rate while the error in the staggered FDTD method is dominated by the first order interface error. I end with the conclusion that the DGTD method requires less computation cost than the staggered FDTD method for the two solutions to have roughly the same accuracy for the more realistic 2D dome model.