Efficient Ordinary Differential Equation-Based Discontinuous Galerkin Method for Viscoelastic Wave Modeling

We present an efficient nonconformal-mesh discontinuous Galerkin (DG) method for elastic wave propagation in viscous media. To include the attenuation and dispersion due to the quality factor in time domain, several sets of auxiliary ordinary differential equations (AODEs) are added. Unlike the conventional auxiliary partial differential equation-based algorithm, this new method is highly parallel with its lossless counterpart, thus requiring much less time and storage consumption. Another superior property of the AODE-based DG method is that a novel exact Riemann solver can be derived, which allows heterogeneous viscoelastic coupling, in addition to accurate coupling with purely elastic media and fluid. Furthermore, thanks to the nonconformal-mesh technique, adaptive hp-refinement and flexible memory allocation for the auxiliary variables are achieved. Numerical results demonstrate the efficiency and accuracy of our method.