High‐order parallel discontinuous Galerkin method for time‐domain acoustic simulations.

Abstract

The modeling of acoustic waves in the time‐domain poses a significant challenge in scientific computing. A promising candidate for solving the three dimensional wave equation is the discontinuous Galerkin (DG) method. Advantages of the DG method are the easy parallelization and a special matrix structure which can reduce the overall time and the computer memory needed for solving the problem. In this study, a high order parallel DG method is investigated. The DG solver is implemented using the C++ programming language. Communication between processors of the parallel computer is performed using the message passing interface. In the solver, the polynomial degree of the basis functions is chosen individually for each element of the computation mesh (up to ninth order polynomials can be used). The unbounded problem is truncated using the perfectly matched layers. The method is evaluated with numerical simulations that are performed on a personal computer cluster.