Error-Driven Dynamical hp-Meshes with the Discontinuous Galerkin Method for Three-Dimensional Wave Propagation Problems

TL;DR

This paper introduces an efficient hp-adaptive Discontinuous Galerkin method for 3D electromagnetic wave simulations, enabling accurate, adaptive full-wave transient analysis with anisotropic refinement and reduced computational costs.

Contribution

It presents a novel hp-adaptive DG method with anisotropic refinement and a new reference solution concept for efficient 3D electromagnetic simulations.

Findings

Achieved adaptive full-wave 3D simulations respecting error tolerances.

Implemented anisotropic refinement in both mesh size and polynomial degree.

Reduced computational costs using reference solution variants.

Abstract

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 transient 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.