Efficient large scale electromagnetic simulations using dynamically adapted meshes with the discontinuous Galerkin method

A framework for performing dynamic mesh adaptation with the discontinuous Galerkin method (DGM) is presented. Adaptations include modifications of the local mesh step size (h$h$-adaptation) and the local degree of the approximating polynomials (p$p$-adaptation) as well as their combination. The computation of the approximation within locally adapted elements is based on projections between finite element spaces (FES), which are shown to preserve an upper limit of the electromagnetic energy. The formulation supports high level hanging nodes and applies precomputation of surface integrals for increasing computational efficiency. Error and smoothness estimates based on interface jumps are presented and applied to the fully hp$hp$-adaptive simulation of two examples in one-dimensional space. A full wave simulation of electromagnetic scattering from a radar reflector demonstrates the applicability to large scale problems in three-dimensional space.