A p -Adaptive Discontinuous Galerkin Method for Solving Second-Order Seismic Wave Equations

Abstract

We present a p-adaptive discontinuous Galerkin (DG) approach for solving second-order elastic and acoustic wave equations. An arbitrary anisotropic medium is considered, and the first- to fourth-order polynomials are used. The second-order wave equation is first transformed into a unified first-order hyperbolic system that is suitable for the DG method. In the following, we describe the p-adaptive DG algorithm in detail. The adaptation criterion using the area indicator is adopted, and the order of polynomial applied for each subdomain in the whole computational domain is marked before time evolution. The adaptation used for wave propagation simulation is practical and flexible, and various numerical fluxes can be directly incorporated into this p-adaptive DG algorithm. Two numerical examples are used to demonstrate the performance of the proposed adaptive scheme.