Efficient Large Scale Electromagnetics Simulations Using Dynamically Adapted Meshes with the Discontinuous Galerkin Method
For computational electromagnetics researchers, this is an incremental extension of existing mesh adaptation techniques to the discontinuous Galerkin method.
The paper presents a framework for dynamic mesh adaptation (h-, p-, and hp-adaptation) with the discontinuous Galerkin method for electromagnetics, demonstrating energy-preserving projections and efficient handling of hanging nodes. It shows applicability to large-scale 3D scattering problems, but provides no quantitative performance gains.
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-adaptation) and the local degree of the approximating polynomials (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-adaptive simulation of two examples in one-dimensional space. A full wave simulation of electromagnetic scattering form a radar reflector demonstrates the applicability to large scale problems in three-dimensional space.