$p$-adaptive algorithms in Discontinuous Galerkin solutions to the time-domain Maxwell's equations

TL;DR

This paper develops and compares two adaptive algorithms for the Discontinuous Galerkin method applied to time-domain Maxwell's equations, focusing on efficiency and accuracy in electromagnetic scattering simulations.

Contribution

It introduces two novel adaptivity drivers—feature-based and divergence error-based—for improved local accuracy in DG solutions of Maxwell's equations.

Findings

Both methods effectively identify regions needing refinement.

The feature-based method improves accuracy in scattering problems.

Divergence error-based method enhances stability and error control.

Abstract

The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to dynamically identify regions and assign spatial operators of varying accuracy in the computational domain. This work identifies requisite properties of adaptivity drivers and develops two methods, a feature-based method guided by gradients of local field, and another utilizing the divergence error often found in numerical solution to the time-domain Maxwell's equations. Results for canonical testcases of electromagnetic scattering are presented, highlighting key characteristics of both methods, and their computational performance.