Efficient Large Scale Electromagnetics Simulations Using Dynamically Adapted Meshes with the Discontinuous Galerkin Method

TL;DR

This paper introduces a dynamic mesh adaptation framework for large-scale electromagnetic simulations using the discontinuous Galerkin method, enhancing efficiency and accuracy in 1D and 3D problems.

Contribution

It presents a novel approach combining h- and p-adaptation with energy-preserving projections, supporting high-level hanging nodes and efficient computations.

Findings

Energy-preserving projections maintain electromagnetic energy bounds.

Successful application to 1D hp-adaptive simulations.

Demonstrated large-scale 3D electromagnetic scattering simulation.

Abstract

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.