The fast and accurate solution of wave propagation problems remains a challenging obstacle in many applications. Low-order polynomial methods typically deliver poor approximations due to dispersion errors, so that specific numerical schemes are required. This minisymposium will bring together a variety of researchers working on this topic, from the design and analysis of numerical methods to the implementation of solvers. A list of speakers who accepted to participate is given in the attached pdf file, together with tentative titles for their presentations.