Contributed Talk
Time discontinuous Galerkin methods for wave propagation problems
Politecnico di Milano, Italy
Abstract
The study of direct and inverse wave propagation phenomena is an area of intensive research and finds important applications in different engineering areas including acoustics, aeroacoustics, electromagnetics, and computational seismology. From the mathematical perspective, the physics governing these phenomena can be modeled by means of the wave equation. From the numerical viewpoint, a number of distinguished challenges arise when tackling such kinds of problems, and reflect onto the following features required to the numerical schemes: accuracy, geometric flexibility, and scalability. In recent years, high order discontinuous Galerkin (dG) methods have become one of the most promising tools for the solution of wave propagation problems. Indeed, thanks to their local nature, dG methods are particularly apt to treat highly heterogeneous media, complex geometries, and sharp variation of the wave field by allowing for space and time adaptivity within the approximation. In this work, we present two different dG schemes that can be applied for the time integration of the system of second-order ordinary differential equations stemming after a dG space discretization of the wave equation. We compare the resulting discrete formulations from the point of view of stability, convergence, and computational cost, highlighting the main advantages and drawbacks of the two approaches. We present a wide set of two- and three-dimensional numerical experiments confirming the theoretical error bounds and apply the methods to realistic geophysical problems. Finally, we analyze the efficiency of the algorithm from the point of view of scalability on HPC machines.