Abstract: Efficient and accurate simulations of wave propagation have a wide range of applications in science and engineering, from seismic and medical imaging to rupture and earthquake simulations. Discontinuous Galerkin (DG) methods enable high order accurate simulations for wave propagation on domains with complex geometries. However, DG methods face several challenges: they can lose stability or high order accuracy in the presence of heterogeneous media or moving meshes, and they become significantly more expensive as the order of approximation increases. In this talk, we review recent developments which enable provably stable, high order accurate, and efficient time-explicit wave simulations in challenging physical and numerical settings, e.g., complex heterogeneous media and moving curved meshes.
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