A roadmap for Generalized Plane Waves and their interpolation properties

This work focuses on the study of partial differential equation (PDE) based basis function for Discontinuous Galerkin methods to solve numerically wave-related boundary value problems with variable coefficients. To tackle constant coefficients, wave-based have been widely studied in literature: they rely concept Trefftz functions, i.e. local solutions governing PDE, using oscillating functions rather than polynomial represent numerical solution. Generalized Plane Waves (GPWs) are an alternative developed which case not available. In a similar way, incorporate information however only approximate since don’t PDE exactly, but approximated PDE. Considering new set PDEs beyond Helmholtz equation, we propose roadmap construction and interpolation properties GPWs. Identifying carefully various steps process, provide algorithm summarize these establish necessary conditions obtain high order corresponding basis.