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We introduce an extended discontinuous Galerkin discretization ofhyperbolic-parabolic problems on multidimensional semi-infinite domains.Building on previous work on the one-dimensional case, we split thestrip-shaped computational domain into a bounded region, discretized by meansof discontinuous finite elements using Legendre basis functions, and anunbounded subdomain, where scaled Laguerre functions are used as a basis.Numerical fluxes at the interface allow for a seamless coupling of the tworegions. The resulting coupling strategy is shown to produce accurate numericalsolutions in tests on both linear and non-linear scalar and vectorial modelproblems. In addition, an efficient absorbing layer can be simulated in thesemi-infinite part of the domain in order to damp outgoing signals withnegligible spurious reflections at the interface. By tuning the scalingparameter of the Laguerre basis functions, the extended DG scheme simulatestransient dynamics over large spatial scales with a substantial reduction incomputational cost at a given accuracy level compared to standard single-domaindiscontinuous finite element techniques.

Efficient hyperbolic-parabolic models on multi-dimensional unbounded domains using an extended DG approach