A Trefftz method whose shape functions are constructed thanks to a high-order DG finite element method
Abstract
We investigate the feasibility of constructing local solutions to the Helmholtz equation thanks to high-order DG finite element approximations of the Dirichlet-to-Neumann operator. This is then used in a Tre↵tz Discontinuous Galerkin method in place of a boundary element method that was successfully applied in [1] to solve the Helmholtz problem in very large domains. We perform comparisons between the two approaches by considering large domains of propagation including heterogeneities.