Error-driven dynamical hp-meshes with the Discontinuous Galerkin Method for three-dimensional wave propagation problems

An hp-adaptive Discontinuous Galerkin Method for electromagnetic wave propagation phenomena in the time domain is proposed. The method is highly efficient and allows for the first time the adaptive full-wave simulation of large, time-dependent problems in three-dimensional space. Refinement is performed anisotropically in the approximation order p and the mesh step size h regardless of the resulting level of hanging nodes. For guiding the adaptation process a variant of the concept of reference solutions with largely reduced computational costs is proposed. The computational mesh is adapted such that a given error tolerance is respected throughout the entire time-domain simulation.